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Journal articles on the topic 'Telegraph process'

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Author: Grafiati

Published: 10 March 2023

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1

NOAKES, RICHARD J. "Telegraphy is an occult art: Cromwell Fleetwood Varley and the diffusion of electricity to the other world." British Journal for the History of Science 32, no. 4 (December 1999): 421–59. http://dx.doi.org/10.1017/s0007087499003763.

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In May 1862 Desmond G. Fitzgerald, the editor of the Electrician, lamented thattelegraphy has been until lately an art occult even to many of the votaries of electrical science. Submarine telegraphy, initiated by a bold and tentative process – the laying of the Dover cable in the year 1850 – opened out a vast field of opportunity both to merit and competency, and to unscrupulous determination. For the purposes of the latter, the field was to be kept close [sic], and science, which can alone be secured by merit, more or less ignored.To Fitzgerald, the ‘occult’ status of the telegraph looked set to continue, with recent reports of scientific counterfeits, unscrupulous electricians and financially motivated saboteurs involved in the telegraphic art. Nevertheless, Fitzgerald reassured his readers that the confidence of ‘those who act for the public’ had been restored by earnest electricians, whose ‘moral cause’ would ultimately be felt and who ‘may be safely trusted even in matters where there is an option between a private interest and a public benefit’. As a prominent crusader for the telegraph, Fitzgerald voiced the concerns of many electricians seeking public confidence and investment in their trade in the wake of the failed submarine telegraphs of the 1850s. The spread of proper knowledge about the telegraph would hinge on securing an adequate supply of backers and the construction of telegraphy as a truly moral cause – an art cleansed of fraudsters, ignoramuses and dogmatists.

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2

Ratanov, Nikita, and Mikhail Turov. "On Local Time for Telegraph Processes." Mathematics 11, no. 4 (February 12, 2023): 934. http://dx.doi.org/10.3390/math11040934.

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The article consists of an introduction into the theory of passage times associated with telegraph processes. Local time for the telegraph process is defined and analysed. We provide some limited results for telegraphic local times.

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3

Pogorui, Anatoliy A., Anatoliy Swishchuk, and Ramón M. Rodríguez-Dagnino. "Transformations of Telegraph Processes and Their Financial Applications." Risks 9, no. 8 (August 17, 2021): 147. http://dx.doi.org/10.3390/risks9080147.

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In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

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4

ORSINGHER, E., and XUELEI ZHAO. "THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS." Chinese Annals of Mathematics 24, no. 01 (January 2003): 45–56. http://dx.doi.org/10.1142/s0252959903000050.

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5

Bshouty, Daoud, Antonio Di Crescenzo, Barbara Martinucci, and Shelemyahu Zacks. "Generalized Telegraph Process with Random Delays." Journal of Applied Probability 49, no. 3 (September 2012): 850–65. http://dx.doi.org/10.1239/jap/1346955338.

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In this paper we study the distribution of the location, at time t, of a particle moving U time units upwards, V time units downwards, and W time units of no movement (idle). These are repeated cyclically, according to independent alternating renewals. The distributions of U, V, and W are absolutely continuous. The velocities are v = +1 upwards, v = -1 downwards, and v = 0 during idle periods. Let Y+(t), Y−(t), and Y0(t) denote the total time in (0, t) of movements upwards, downwards, and no movements, respectively. The exact distribution of Y+(t) is derived. We also obtain the probability law of X(t) = Y+(t) - Y−(t), which describes the particle's location at time t. Explicit formulae are derived for the cases of exponential distributions with equal rates, with different rates, and with linear rates (leading to damped processes).

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6

Di Crescenzo, Antonio, Antonella Iuliano, Barbara Martinucci, and Shelemyahu Zacks. "Generalized Telegraph Process with Random Jumps." Journal of Applied Probability 50, no. 2 (June 2013): 450–63. http://dx.doi.org/10.1239/jap/1371648953.

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We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

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7

Bshouty, Daoud, Antonio Di Crescenzo, Barbara Martinucci, and Shelemyahu Zacks. "Generalized Telegraph Process with Random Delays." Journal of Applied Probability 49, no. 03 (September 2012): 850–65. http://dx.doi.org/10.1017/s002190020000958x.

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In this paper we study the distribution of the location, at time t, of a particle moving U time units upwards, V time units downwards, and W time units of no movement (idle). These are repeated cyclically, according to independent alternating renewals. The distributions of U, V, and W are absolutely continuous. The velocities are v = +1 upwards, v = -1 downwards, and v = 0 during idle periods. Let Y +(t), Y −(t), and Y 0(t) denote the total time in (0, t) of movements upwards, downwards, and no movements, respectively. The exact distribution of Y +(t) is derived. We also obtain the probability law of X(t) = Y +(t) - Y −(t), which describes the particle's location at time t. Explicit formulae are derived for the cases of exponential distributions with equal rates, with different rates, and with linear rates (leading to damped processes).

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8

Di Crescenzo, Antonio, Antonella Iuliano, Barbara Martinucci, and Shelemyahu Zacks. "Generalized Telegraph Process with Random Jumps." Journal of Applied Probability 50, no. 02 (June 2013): 450–63. http://dx.doi.org/10.1017/s0021900200013486.

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We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at timet=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed timet, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

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9

D'Arrigo, A., G. Falci, and E. Paladino. "Dynamical decoupling of random telegraph noise in a two-qubit gate." International Journal of Quantum Information 12, no. 02 (March 2014): 1461008. http://dx.doi.org/10.1142/s0219749914610085.

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Controlling the dynamics of entanglement and preventing its disappearance are central requisites for any implementation of quantum information processing. Solid state qubits are frequently affected by random telegraph noise due to bistable impurities of different nature coupled to the device. In this paper, we investigate the possibility to achieve an efficient universal two-qubit gate in the presence of random telegraph noise by periodic dynamical decoupling. We find an analytic form of the gate error as a function of the number of applied pulses valid when the gate time is much shorter then the telegraphic process correlation time. The analysis is further supplemented by exact numerical results demonstrating the feasibility of a highly-efficient universal two-qubit gate.

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10

Woods, Robert O. "A Cable to Shrink the Earth." Mechanical Engineering 133, no. 01 (January 1, 2011): 40–44. http://dx.doi.org/10.1115/1.2011-jan-5.

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This article discusses how the invention of the telegram revolutionized the communication process in the mid-19th century. On August 15, 1858, Queen Victoria sent a telegram to President Buchanan. It was a joint American and British effort, spearheaded from the American side by an indefatigable financier, Cyrus West Field, and on the British side by a telegraph company. The message of 98 words took sixteen and a half hours to transmit. The cable that carried Victoria’s message was laid in two sections beginning from a rendezvous point in mid-Atlantic. Two converted battleships spliced their cargoes and parted laying cable; the Agamemnon provided by the British government steered east to Ireland, and the American Niagara west to Newfoundland. Before this cable was laid, there was no direct communication between continents. No message could travel faster than the fastest steamships, which required at least 10 days to make the sea voyage between America and Europe. The submarine telegraph cable reduced communication time from days to hours.

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11

Khasminskii, Rafail Z., and Yury A. Kutoyants. "On parameter estimation of hidden telegraph process." Bernoulli 24, no. 3 (August 2018): 2064–90. http://dx.doi.org/10.3150/16-bej920.

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12

Iacus, S. M., and N. Yoshida. "Estimation for the discretely observed telegraph process." Theory of Probability and Mathematical Statistics 78 (2009): 37–47. http://dx.doi.org/10.1090/s0094-9000-09-00760-1.

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13

Bogachev, Leonid, and Nikita Ratanov. "Occupation time distributions for the telegraph process." Stochastic Processes and their Applications 121, no. 8 (August 2011): 1816–44. http://dx.doi.org/10.1016/j.spa.2011.03.016.

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14

Ratanov, Nikita, Antonio Di Crescenzo, and Barbara Martinucci. "Piecewise deterministic processes following two alternating patterns." Journal of Applied Probability 56, no. 4 (December 2019): 1006–19. http://dx.doi.org/10.1017/jpr.2019.58.

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AbstractWe propose a wide generalization of known results related to the telegraph process. Functionals of the simple telegraph process on a straight line and their generalizations on an arbitrary state space are studied.

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15

Martinucci, Barbara, and Alessandra Meoli. "Certain functionals of squared telegraph processes." Stochastics and Dynamics 20, no. 01 (June 11, 2019): 2050005. http://dx.doi.org/10.1142/s0219493720500057.

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We investigate the stochastic process defined as the square of the (integrated) symmetric telegraph process. Specifically, we obtain its probability law and a closed form expression of the moment generating function. Some results on the first-passage time through a fixed positive level are also provided. Moreover, we analyze some functionals [Formula: see text] of two independent squared telegraph processes, both in the case [Formula: see text] and [Formula: see text]. Starting from this study, we provide some results on the probability density functions of the two-dimensional radial telegraph process and of the product of two independent symmetric telegraph processes. Some of the expressions obtained are given in terms of new results about derivatives of hypergeometric functions with respect to parameters.

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16

Surur, Agus Miftakus, Yudi Ari Adi, and Sugiyanto Sugiyanto. "Penyelesaian Persamaan Telegraph Dan Simulasinya." Jurnal Fourier 2, no. 1 (April 1, 2013): 33. http://dx.doi.org/10.14421/fourier.2013.21.33-43.

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Equation Telegraph is one of type from wave equation. Solving of the wave equation obtainable by using Green's function with the method of boundary condition problem. This research aim to to show the process obtain;get the mathematical formula from wave equation and also know the form of solution of wave equation by using Green's function. Result of analysis indicate that the process get the mathematical formula from wave equation from applicable Green's function in equation which deal with the wave equation, that is applied in equation Telegraph. Solution started with searching public form from Green's function, hereinafter look for the solving of wave equation in Green's function. Application from the wave equation used to look for the solving of equation Telegraph. Result from equation Telegraph which have been obtained will be shown in the form of picture (knowable to simulasi) so that form of the the equation Telegraph.

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17

Kielbowicz, Richard B. "Electrifying news! Journalists, audiences, and the culture of timeliness in the United States, 1840--1920." Time & Society 28, no. 1 (March 3, 2016): 200–230. http://dx.doi.org/10.1177/0961463x16634724.

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The telegraph literally and figuratively electrified news by transforming reporting into a process that delivered impulses of information whose timeliness often riveted and sometimes excited newspaper audiences. The now-familiar daily news cycle—scheduled reports of recent news punctuated by even more timely breaking news—originated with telegraphic journalism. Daily papers began presenting themselves as the public’s portal to an electrified national and international newsgathering network. Looking beyond the role of telegraph firms and wire services, this study explores how the culture of journalistic timeliness was cultivated in organizational, occupational, and public settings. Organizationally, telegraph-enabled timeliness altered every stage of the news-production process, from reporter-source interactions to the delivery of stories to readers. The press reified timeliness internally through organizational rewards and occupational discourses, and externally by projecting its institutional values through marketing and the metatexts that accompanied stories. For the audience, daily papers conveyed the temporal rhythms of a networked industrial society. Audiences valued some timely news as data inputs that enhanced opportunities to participate in distant affairs or influence outcomes, though for economic intelligence private channels almost always outstripped newspapers’ public delivery of the same information. But even electrified news valued mostly for its storytelling made events common to many people simultaneously in a manner that encouraged the construction of meaning by scattered audiences. In those situations, timeliness often meant that news circulated fast enough for reactions around the nation to become part of the story itself.

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18

Di Crescenzo, Antonio, and Barbara Martinucci. "On the Generalized Telegraph Process with Deterministic Jumps." Methodology and Computing in Applied Probability 15, no. 1 (June 19, 2011): 215–35. http://dx.doi.org/10.1007/s11009-011-9235-x.

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19

Di Crescenzo, Antonio, Barbara Martinucci, and Shelemyahu Zacks. "Telegraph Process with Elastic Boundary at the Origin." Methodology and Computing in Applied Probability 20, no. 1 (March 3, 2017): 333–52. http://dx.doi.org/10.1007/s11009-017-9549-4.

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20

Orsingher, Enzo. "Random motions governed by third-order equations." Advances in Applied Probability 22, no. 04 (December 1990): 915–28. http://dx.doi.org/10.1017/s0001867800023193.

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In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation. We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process. Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

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21

Orsingher, Enzo. "Random motions governed by third-order equations." Advances in Applied Probability 22, no. 4 (December 1990): 915–28. http://dx.doi.org/10.2307/1427568.

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In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation.We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process.Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

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22

Khoa, Doan Quoc, Chu Van Lanh, Phan Xuan Sanh, Nguyen Thi Hong Sang, Le Thi Hoa, Nguyen Thi Thu, and Bui Van Dung. "An Exactly Soluble Equation for the Stationary Probability Distribution in a Nonlinear System under the Influence of Two-telegraph Noise: Application to the Noise Reduction in a Raman Ring Laser." Communications in Physics 26, no. 1 (July 18, 2016): 75. http://dx.doi.org/10.15625/0868-3166/26/1/8352.

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In this paper, we will consider a model of nonlinear system with random telegraph noises and a Raman ring laser by modeling the laser pump light by a pregaussian process and find an exactly soluble equations for the stationary probability distribution of fluctuations in this nonlinear system under the influence of two-telegraph noise. In consequence, we will obtain the so-called noise reduction in this system: the Stokes output of this laser tends to the stabilize under the influence of the broad-band two-telegraph pregaussian pump and compare this results with that obtained in our previous paper (Cao Long Van, Doan Quoc Khoa, Opt. Quant. Electron. 43, 137 (2012)) for the case of one telegraph noise.

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23

Di Crescenzo, Antonio, and Alessandra Meoli. "On a jump-telegraph process driven by an alternating fractional Poisson process." Journal of Applied Probability 55, no. 1 (March 2018): 94–111. http://dx.doi.org/10.1017/jpr.2018.8.

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AbstractThe basic jump-telegraph process with exponentially distributed interarrival times deserves interest in various applied fields such as financial modelling and queueing theory. Aiming to propose a more general setting, we analyse such a stochastic process when the interarrival times separating consecutive velocity changes (and jumps) have generalized Mittag-Leffler distributions, and constitute the random times of a fractional alternating Poisson process. By means of renewal theory-based issues we obtain the forward and backward transition densities of the motion in series form, and prove their uniform convergence. Specific attention is then given to the case of jumps with constant size, for which we also obtain the mean of the process. Finally, we investigate the first-passage time of the process through a constant positive boundary, providing its formal distribution and suitable lower bounds.

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24

Di Crescenzo, Antonio, and Barbara Martinucci. "A Damped Telegraph Random Process with Logistic Stationary Distribution." Journal of Applied Probability 47, no. 1 (March 2010): 84–96. http://dx.doi.org/10.1239/jap/1269610818.

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We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given.

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25

Di Crescenzo, Antonio, and Barbara Martinucci. "A Damped Telegraph Random Process with Logistic Stationary Distribution." Journal of Applied Probability 47, no. 01 (March 2010): 84–96. http://dx.doi.org/10.1017/s0021900200006410.

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We introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given.

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26

Pozdnyakov, Vladimir, L. Mark Elbroch, Anthony Labarga, Thomas Meyer, and Jun Yan. "Discretely Observed Brownian Motion Governed by Telegraph Process: Estimation." Methodology and Computing in Applied Probability 21, no. 3 (February 2, 2017): 907–20. http://dx.doi.org/10.1007/s11009-017-9547-6.

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27

Stadje, W., and S. Zacks. "Telegraph processes with random velocities." Journal of Applied Probability 41, no. 03 (September 2004): 665–78. http://dx.doi.org/10.1017/s0021900200020465.

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We study a one-dimensional telegraph process (Mt)t≥0describing the position of a particle moving at constant speed between Poisson times at which new velocities are chosen randomly. The exact distribution ofMtand its first two moments are derived. We characterize the level hitting times ofMtin terms of integro-differential equations which can be solved in special cases.

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28

Stadje, W., and S. Zacks. "Telegraph processes with random velocities." Journal of Applied Probability 41, no. 3 (September 2004): 665–78. http://dx.doi.org/10.1239/jap/1091543417.

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We study a one-dimensional telegraph process (Mt)t≥0 describing the position of a particle moving at constant speed between Poisson times at which new velocities are chosen randomly. The exact distribution of Mt and its first two moments are derived. We characterize the level hitting times of Mt in terms of integro-differential equations which can be solved in special cases.

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29

Di Matteo, Ilaria, and Enzo Orsingher. "Detailed probabilistic analysis of the integrated three-valued telegraph signal." Journal of Applied Probability 34, no. 3 (September 1997): 671–84. http://dx.doi.org/10.2307/3215093.

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In this paper the integrated three-valued telegraph process is examined. In particular, the third-order equations governing the distributions , (where N(t) denotes the number of changes of the telegraph process up to time t) are derived and recurrence relationships for them are obtained by solving suitable initial-value problems. These recurrence formulas are related to the Fourier transform of the conditional distributions and are used to obtain explicit results for small values of k. The conditional mean values (where V(0) denotes the initial velocity of motions) are obtained and discussed.

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30

Di Matteo, Ilaria, and Enzo Orsingher. "Detailed probabilistic analysis of the integrated three-valued telegraph signal." Journal of Applied Probability 34, no. 03 (September 1997): 671–84. http://dx.doi.org/10.1017/s0021900200101330.

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In this paper the integrated three-valued telegraph process is examined. In particular, the third-order equations governing the distributions , (where N(t) denotes the number of changes of the telegraph process up to time t) are derived and recurrence relationships for them are obtained by solving suitable initial-value problems. These recurrence formulas are related to the Fourier transform of the conditional distributions and are used to obtain explicit results for small values of k. The conditional mean values (where V(0) denotes the initial velocity of motions) are obtained and discussed.

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31

Beghin, L., L. Nieddu, and E. Orsingher. "Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations." Journal of Applied Mathematics and Stochastic Analysis 14, no. 1 (January 1, 2001): 11–25. http://dx.doi.org/10.1155/s104895330100003x.

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The telegrapher's process with drift is here examined and its distribution is obtained by applying the Lorentz transformation. The related characteristic function as well as the distribution are also derived by solving an initial value problem for the generalized telegraph equation.

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32

HERRMANN, S., and P. VALLOIS. "FROM PERSISTENT RANDOM WALK TO THE TELEGRAPH NOISE." Stochastics and Dynamics 10, no. 02 (June 2010): 161–96. http://dx.doi.org/10.1142/s0219493710002905.

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We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process (Zt) which can be easily expressed in terms of a counting process (Nt). In a particular case the counting process is a Poisson process, and (Zt) permits to represent the solution of the telegraph equation. We study in detail the Markov process ((Zt, Nt); t ≥ 0).

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33

Wang, Fuzhang, and Enran Hou. "A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations." Journal of Mathematics 2020 (November 10, 2020): 1–9. http://dx.doi.org/10.1155/2020/8832197.

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In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.

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34

López, Oscar, and Nikita Ratanov. "Option Pricing Driven by a Telegraph Process with Random Jumps." Journal of Applied Probability 49, no. 3 (September 2012): 838–49. http://dx.doi.org/10.1239/jap/1346955337.

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In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

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35

López, Oscar, and Nikita Ratanov. "Option Pricing Driven by a Telegraph Process with Random Jumps." Journal of Applied Probability 49, no. 03 (September 2012): 838–49. http://dx.doi.org/10.1017/s0021900200009578.

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In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

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36

Cinque, F., and E. Orsingher. "On the distribution of the maximum of the telegraph process." Theory of Probability and Mathematical Statistics 102 (March 29, 2021): 73–95. http://dx.doi.org/10.1090/tpms/1128.

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37

Pospelov, I. G., and S. A. Radionov. "Optimal Dividend Policy when Cash Surplus Follows the Telegraph Process." Mathematical Notes 109, no. 1-2 (January 2021): 125–35. http://dx.doi.org/10.1134/s0001434621010156.

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38

Cinque, Fabrizio. "A note on the conditional probabilities of the telegraph process." Statistics & Probability Letters 185 (June 2022): 109431. http://dx.doi.org/10.1016/j.spl.2022.109431.

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39

Crimaldi, Irene, Antonio Di Crescenzo, Antonella Iuliano, and Barbara Martinucci. "A Generalized Telegraph Process with Velocity Driven by Random Trials." Advances in Applied Probability 45, no. 4 (December 2013): 1111–36. http://dx.doi.org/10.1239/aap/1386857860.

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We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

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40

Crimaldi, Irene, Antonio Di Crescenzo, Antonella Iuliano, and Barbara Martinucci. "A Generalized Telegraph Process with Velocity Driven by Random Trials." Advances in Applied Probability 45, no. 04 (December 2013): 1111–36. http://dx.doi.org/10.1017/s0001867800006790.

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We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

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Balmori, Diana. "George B. Post: The Process of Design and the New American Architectural Office (1868-1913)." Journal of the Society of Architectural Historians 46, no. 4 (December 1, 1987): 342–55. http://dx.doi.org/10.2307/990273.

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This article deals with an American architect, George B. Post, and the organization of his office. Post's practice was one of the earliest to be conducted as an office rather than an atelier. It was also the first large architectural practice based on what came to be considered the prototypical American building, the office tower. The article examines the organization of Post's office, the way work was done, the building types designed, and the nature of its clients. It concentrates on the design process of one particular building, the Western Union Telegraph Building in New York, which was pivotal not only for this practice but for American architecture. The Western Union Telegraph Building was an early example of the national corporate headquarters and, if it was not the first skyscraper, then it certainly was its immediate precursor.

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Strekalova, Natalya V., and Sergey V. Shcherbakov. "Employees of communications institutions of the Tambov Governorate in the second half of the 19th – early 20th centuries: number, staff, professional mobility." Tambov University Review. Series: Humanities, no. 188 (2020): 164–75. http://dx.doi.org/10.20310/1810-0201-2020-25-188-164-175.

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The role and importance of information and communication infrastructure in the modern world is growing, which increases the relevance of studying the history of the formation and development of postal, telegraph and telephone communications in Russia, primarily regional features of the social component of this process. Based on interdisciplinary approaches, involving a wide range of historical sources, the work explores the problems of the postal, telegraph and telephone service in the Tambov Governorate in the second half of the 19th – early 20th centuries. The issues of the number and staff of employees in communication institutions (post office, telegraph, telephone) of the Tambov Governorate are studied. We reveal the peculiarities and problems of the development of institutions staff of the postal and telegraph department. The problems of professional mobility of postal and telegraph employees are analyzed; the requirements for them, their official duties are described. In the second half of the 19th – early 20th century in the social and economic life of the Russian province, the information and communication component began to play a prominent role, which was reflected in the increase in the number of communica-tion institutions in the Tambov Governorate and employees in them. There were acute issues of human resourcing, first of all, qualified specialists. At the beginning of the 20th century the pro-portion of women who served in the institutions of the postal and telegraph department of the go-vernorate increased.

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Melnyk, Sergei A., and Anna A. Kharkhota. "Differential Representation of a Samuelson Model with a Telegraph Drift." Tatra Mountains Mathematical Publications 69, no. 1 (June 27, 2017): 45–59. http://dx.doi.org/10.1515/tmmp-2017-0013.

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Abstract In this paper we construct a system of three stochastic differential equations, which has a solution composed of a generalized telegraph signal process and a basic process. This system enabled us to find the escape probability of the basic process from an interval through its endpoint.

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Orsingher, Enzo, and Bruno Bassan. "On a 2n-valued telegraph signal and the related integrated process." Stochastics and Stochastic Reports 38, no. 3 (March 1992): 159–73. http://dx.doi.org/10.1080/17442509208833753.

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45

Tilles, Paulo F. C., and Sergei V. Petrovskii. "On the Consistency of the Reaction-Telegraph Process Within Finite Domains." Journal of Statistical Physics 177, no. 4 (September 5, 2019): 569–87. http://dx.doi.org/10.1007/s10955-019-02379-0.

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Borodin, A. N. "Joint Distributions of Functionals of the Telegraph Process and Switching Diffusions." Journal of Mathematical Sciences 244, no. 5 (January 9, 2020): 723–32. http://dx.doi.org/10.1007/s10958-020-04645-z.

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47

Michelitsch, Thomas M., Federico Polito, and Alejandro P. Riascos. "Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times." Mathematics 11, no. 2 (January 16, 2023): 471. http://dx.doi.org/10.3390/math11020471.

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In a recent work we introduced a semi-Markovian discrete-time generalization of the telegraph process. We referred to this random walk as the ‘squirrel random walk’ (SRW). The SRW is a discrete-time random walk on the one-dimensional infinite lattice where the step direction is reversed at arrival times of a discrete-time renewal process and remains unchanged at uneventful time instants. We first recall general notions of the SRW. The main subject of the paper is the study of the SRW where the step direction switches at the arrival times of a generalization of the Sibuya discrete-time renewal process (GSP) which only recently appeared in the literature. The waiting time density of the GSP, the ‘generalized Sibuya distribution’ (GSD), is such that the moments are finite up to a certain order r≤m−1 (m≥1) and diverging for orders r≥m capturing all behaviors from broad to narrow and containing the standard Sibuya distribution as a special case (m=1). We also derive some new representations for the generating functions related to the GSD. We show that the generalized Sibuya SRW exhibits several regimes of anomalous diffusion depending on the lowest order m of diverging GSD moment. The generalized Sibuya SRW opens various new directions in anomalous physics.

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Vergara, Vicente. "Asymptotic Behaviour of the Time-Fractional Telegraph Equation." Journal of Applied Probability 51, no. 3 (September 2014): 890–93. http://dx.doi.org/10.1239/jap/1409932682.

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We obtain the long-time behaviour to the variance of the distribution process associated with the solution of the telegraph equation. To this end, we use a version of the Karamata-Feller Tauberian theorem.

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Vergara, Vicente. "Asymptotic Behaviour of the Time-Fractional Telegraph Equation." Journal of Applied Probability 51, no. 03 (September 2014): 890–93. http://dx.doi.org/10.1017/s002190020001175x.

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We obtain the long-time behaviour to the variance of the distribution process associated with the solution of the telegraph equation. To this end, we use a version of the Karamata-Feller Tauberian theorem.

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50

Orsingher, Enzo. "On the Vector Process Obtained by Iterated Integration of the Telegraph Signal." gmj 6, no. 2 (April 1999): 169–78. http://dx.doi.org/10.1515/gmj.1999.169.

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Abstract We analyse the vector process (𝑋0(𝑡),𝑋1(𝑡), . . . , 𝑋𝑛(𝑡), 𝑡 > 0) where , 𝑘 = 1, . . . , 𝑛, and 𝑋0(𝑡) is the two-valued telegraph process. In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed. Special care is given to the case of the process (𝑋0(𝑡),𝑋1(𝑡),𝑋2(𝑡), 𝑡 > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.

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