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Journal articles on the topic 'Continuous Time Processes'

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Author: Grafiati

Published: 10 March 2023

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1

Brockwell, Peter, Erdenebaatar Chadraa, and Alexander Lindner. "Continuous-time GARCH processes." Annals of Applied Probability 16, no. 2 (May 2006): 790–826. http://dx.doi.org/10.1214/105051606000000150.

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2

Torsello, Andrea, and Marcello Pelillo. "Continuous-time relaxation labeling processes." Pattern Recognition 33, no. 11 (November 2000): 1897–908. http://dx.doi.org/10.1016/s0031-3203(99)00174-0.

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3

Brockwell, Peter J., Jens-Peter Kreiss, and Tobias Niebuhr. "Bootstrapping continuous-time autoregressive processes." Annals of the Institute of Statistical Mathematics 66, no. 1 (May 9, 2013): 75–92. http://dx.doi.org/10.1007/s10463-013-0406-0.

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4

Viano, M. C., C. Deniau, and G. Oppenheim. "Continuous-time fractional ARMA processes." Statistics & Probability Letters 21, no. 4 (November 1994): 323–36. http://dx.doi.org/10.1016/0167-7152(94)00015-8.

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5

Li, Quan-Lin, and Chuang Lin. "Continuous-Time QBD Processes with Continuous Phase Variable." Computers & Mathematics with Applications 52, no. 10-11 (November 2006): 1483–510. http://dx.doi.org/10.1016/j.camwa.2006.07.003.

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6

González, Miguel, Manuel Molina, Ines del Puerto, Nikolay M. Yanev, and George P. Yanev. "Controlled branching processes with continuous time." Journal of Applied Probability 58, no. 3 (September 2021): 830–48. http://dx.doi.org/10.1017/jpr.2021.8.

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AbstractA class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

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7

Stramer, O., P. J. Brockwell, and R. L. Tweedie. "Continuous-time threshold AR(1) processes." Advances in Applied Probability 28, no. 3 (September 1996): 728–46. http://dx.doi.org/10.2307/1428178.

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A threshold AR(1) process with boundary width 2δ > 0 was defined by Brockwell and Hyndman [5] in terms of the unique strong solution of a stochastic differential equation whose coefficients are piecewise linear and Lipschitz. The positive boundary-width is a convenient mathematical device to smooth out the coefficient changes at the boundary and hence to ensure the existence and uniqueness of the strong solution of the stochastic differential equation from which the process is derived. In this paper we give a direct definition of a threshold AR(1) process with δ = 0 in terms of the weak solution of a certain stochastic differential equation. Two characterizations of the distributions of the process are investigated. Both express the characteristic function of the transition probability distribution as an explicit functional of standard Brownian motion. It is shown that the joint distributions of this solution with δ = 0 are the weak limits as δ ↓ 0 of the distributions of the solution with δ > 0. The sense in which an approximating sequence of processes used by Brockwell and Hyndman [5] converges to this weak solution is also investigated. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the process obtained from the Cameron–Martin–Girsanov formula and results of Engelbert and Schmidt [9]. We also derive the stationary distribution (under appropriate assumptions) and investigate stability of these processes.

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8

Irle, A. "Stochastic ordering for continuous-time processes." Journal of Applied Probability 40, no. 2 (June 2003): 361–75. http://dx.doi.org/10.1239/jap/1053003549.

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We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Yt)t is said to be slower in level crossing than a process (Zt)t if it takes (Yt)t stochastically longer than (Zt)t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.

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9

Brockwell, Peter J. "Representations of continuous-time ARMA processes." Journal of Applied Probability 41, A (2004): 375–82. http://dx.doi.org/10.1239/jap/1082552212.

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Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.

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10

Tian, Jianjun, and Xiao-Song Lin. "Continuous Time Markov Processes on Graphs." Stochastic Analysis and Applications 24, no. 5 (September 22, 2006): 953–72. http://dx.doi.org/10.1080/07362990600870017.

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11

Brockwell, Peter J. "Representations of continuous-time ARMA processes." Journal of Applied Probability 41, A (2004): 375–82. http://dx.doi.org/10.1017/s0021900200112422.

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Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.

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12

Irle, A. "Stochastic ordering for continuous-time processes." Journal of Applied Probability 40, no. 02 (June 2003): 361–75. http://dx.doi.org/10.1017/s0021900200019355.

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We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Y t ) t is said to be slower in level crossing than a process (Z t ) t if it takes (Y t ) t stochastically longer than (Z t ) t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.

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13

Stramer, O., P. J. Brockwell, and R. L. Tweedie. "Continuous-time threshold AR(1) processes." Advances in Applied Probability 28, no. 03 (September 1996): 728–46. http://dx.doi.org/10.1017/s0001867800046462.

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Abstract:

A threshold AR(1) process with boundary width 2δ > 0 was defined by Brockwell and Hyndman [5] in terms of the unique strong solution of a stochastic differential equation whose coefficients are piecewise linear and Lipschitz. The positive boundary-width is a convenient mathematical device to smooth out the coefficient changes at the boundary and hence to ensure the existence and uniqueness of the strong solution of the stochastic differential equation from which the process is derived. In this paper we give a direct definition of a threshold AR(1) process with δ = 0 in terms of the weak solution of a certain stochastic differential equation. Two characterizations of the distributions of the process are investigated. Both express the characteristic function of the transition probability distribution as an explicit functional of standard Brownian motion. It is shown that the joint distributions of this solution with δ = 0 are the weak limits as δ ↓ 0 of the distributions of the solution with δ > 0. The sense in which an approximating sequence of processes used by Brockwell and Hyndman [5] converges to this weak solution is also investigated. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the process obtained from the Cameron–Martin–Girsanov formula and results of Engelbert and Schmidt [9]. We also derive the stationary distribution (under appropriate assumptions) and investigate stability of these processes.

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14

Muliere, Pietro, Piercesare Secchi, and Stephen G. Walker. "Reinforced random processes in continuous time." Stochastic Processes and their Applications 104, no. 1 (March 2003): 117–30. http://dx.doi.org/10.1016/s0304-4149(02)00234-x.

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15

Brockwell, P. J. "On continuous-time threshold ARMA processes." Journal of Statistical Planning and Inference 39, no. 2 (April 1994): 291–303. http://dx.doi.org/10.1016/0378-3758(94)90210-0.

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16

Davis, Burgess, and Stanislav Volkov. "Continuous time vertex-reinforced jump processes." Probability Theory and Related Fields 123, no. 2 (June 1, 2002): 281–300. http://dx.doi.org/10.1007/s004400100189.

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17

Budhiraja, Amarjit, Paul Dupuis, and Vasileios Maroulas. "Variational representations for continuous time processes." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 47, no. 3 (August 2011): 725–47. http://dx.doi.org/10.1214/10-aihp382.

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18

Stock, James H. "Estimating Continuous-Time Processes Subject to Time Deformation." Journal of the American Statistical Association 83, no. 401 (March 1988): 77–85. http://dx.doi.org/10.1080/01621459.1988.10478567.

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19

Chambers, Marcus J., and Michael A. Thornton. "DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES." Econometric Theory 28, no. 1 (August 2, 2011): 219–38. http://dx.doi.org/10.1017/s0266466611000181.

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This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

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20

Desharnais, Josée, and Prakash Panangaden. "Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes." Journal of Logic and Algebraic Programming 56, no. 1-2 (May 2003): 99–115. http://dx.doi.org/10.1016/s1567-8326(02)00068-1.

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21

Shelton, C. R., and G. Ciardo. "Tutorial on Structured Continuous-Time Markov Processes." Journal of Artificial Intelligence Research 51 (December 23, 2014): 725–78. http://dx.doi.org/10.1613/jair.4415.

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A continuous-time Markov process (CTMP) is a collection of variables indexed by a continuous quantity, time. It obeys the Markov property that the distribution over a future variable is independent of past variables given the state at the present time. We introduce continuous-time Markov process representations and algorithms for filtering, smoothing, expected sufficient statistics calculations, and model estimation, assuming no prior knowledge of continuous-time processes but some basic knowledge of probability and statistics. We begin by describing "flat" or unstructured Markov processes and then move to structured Markov processes (those arising from state spaces consisting of assignments to variables) including Kronecker, decision-diagram, and continuous-time Bayesian network representations. We provide the first connection between decision-diagrams and continuous-time Bayesian networks.

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22

Bibi, Abdelouahab, and Fateh Merahi. "GMM Estimation of Continuous-Time Bilinear Processes." Statistics, Optimization & Information Computing 9, no. 4 (October 8, 2020): 990–1009. http://dx.doi.org/10.19139/soic-2310-5070-902.

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This paper examines the moments properties in frequency domain of the class of first order continuous-timebilinear processes (COBL(1,1) for short) with time-varying (resp. time-invariant) coefficients. So, we used theassociated evolutionary (or time-varying) transfer functions to study the structure of second-order of the process and its powers. In particular, for time-invariant case, an expression of the moments of any order are showed and the continuous-time AR (CAR) representation of COBL(1,1) is given as well as some moments properties of special cases. Based on these results we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM) illustrated by a Monte Carlo study and applied to modelling two foreign exchange rates of Algerian Dinar against U.S-Dollar (USD/DZD) and against the single European currency Euro (EUR/DZD).

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23

Jeong, Minsoo. "Modelling persistent stationary processes in continuous time." Economic Modelling 109 (April 2022): 105776. http://dx.doi.org/10.1016/j.econmod.2022.105776.

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24

Vijverberg, Chu-Ping C. "Time Deformation, Continuous Euler Processes and Forecasting." Journal of Time Series Analysis 27, no. 6 (November 2006): 811–29. http://dx.doi.org/10.1111/j.1467-9892.2006.00490.x.

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25

Lyman, R. J., W. W. Edmonson, S. McCullough, and M. Rao. "The predictability of continuous-time, bandlimited processes." IEEE Transactions on Signal Processing 48, no. 2 (2000): 311–16. http://dx.doi.org/10.1109/78.823959.

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26

Heidergott, Bernd, Arie Hordijk, and Nicole Leder. "Series Expansions for Continuous-Time Markov Processes." Operations Research 58, no. 3 (June 2010): 756–67. http://dx.doi.org/10.1287/opre.1090.0738.

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27

Debbarh, Mohammed, and Bertrand Maillot. "Additive Regression Model for Continuous Time Processes." Communications in Statistics - Theory and Methods 37, no. 15 (June 11, 2008): 2416–32. http://dx.doi.org/10.1080/03610920801919676.

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28

Samorodnitsky, Gennady. "Maxima of continuous-time stationary stable processes." Advances in Applied Probability 36, no. 3 (September 2004): 805–23. http://dx.doi.org/10.1239/aap/1093962235.

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We study the suprema over compact time intervals of stationary locally bounded α-stable processes. The behaviour of these suprema as the length of the time interval increases turns out to depend significantly on the ergodic-theoretical properties of a flow generating the stationary process.

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29

Dai Pra, Paolo, Pierre-Yves Louis, and Ida Germana Minelli. "Realizable monotonicity for continuous-time Markov processes." Stochastic Processes and their Applications 120, no. 6 (June 2010): 959–82. http://dx.doi.org/10.1016/j.spa.2010.03.002.

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30

Samorodnitsky, Gennady. "Maxima of continuous-time stationary stable processes." Advances in Applied Probability 36, no. 03 (September 2004): 805–23. http://dx.doi.org/10.1017/s0001867800013124.

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We study the suprema over compact time intervals of stationary locally bounded α-stable processes. The behaviour of these suprema as the length of the time interval increases turns out to depend significantly on the ergodic-theoretical properties of a flow generating the stationary process.

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31

Chacko, George, and Luis M. Viceira. "Spectral GMM estimation of continuous-time processes." Journal of Econometrics 116, no. 1-2 (September 2003): 259–92. http://dx.doi.org/10.1016/s0304-4076(03)00109-x.

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32

Eberlein, Ernst. "Strong approximation of continuous time stochastic processes." Journal of Multivariate Analysis 31, no. 2 (November 1989): 220–35. http://dx.doi.org/10.1016/0047-259x(89)90063-8.

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33

Levanony, David, Adam Shwartz, and Ofer Zeitouni. "Recursive identification in continuous-time stochastic processes." Stochastic Processes and their Applications 49, no. 2 (February 1994): 245–75. http://dx.doi.org/10.1016/0304-4149(94)90137-6.

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34

Houba, Harold. "On continuous-time Markov processes in bargaining." Economics Letters 100, no. 2 (August 2008): 280–83. http://dx.doi.org/10.1016/j.econlet.2008.02.009.

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35

Berkowitz, Jeremy. "On Identification of Continuous Time Stochastic Processes." Finance and Economics Discussion Series 2000, no. 07 (March 2000): 1–16. http://dx.doi.org/10.17016/feds.2000.07.

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36

Puterman, Martin L., and F. A. Van der Duyn Schouten. "Markov Decision Processes With Continuous Time Parameter." Journal of the American Statistical Association 80, no. 390 (June 1985): 491. http://dx.doi.org/10.2307/2287942.

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37

Cseke, Botond, David Schnoerr, Manfred Opper, and Guido Sanguinetti. "Expectation propagation for continuous time stochastic processes." Journal of Physics A: Mathematical and Theoretical 49, no. 49 (November 14, 2016): 494002. http://dx.doi.org/10.1088/1751-8113/49/49/494002.

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38

Aı¨t-Sahalia, Yacine, and Jialin Yu. "Saddlepoint approximations for continuous-time Markov processes." Journal of Econometrics 134, no. 2 (October 2006): 507–51. http://dx.doi.org/10.1016/j.jeconom.2005.07.004.

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39

He, Qi-Ming. "Construction of continuous time Markovian arrival processes." Journal of Systems Science and Systems Engineering 19, no. 3 (August 27, 2010): 351–66. http://dx.doi.org/10.1007/s11518-010-5139-5.

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40

Comte, F., and E. Renault. "Noncausality in Continuous Time Models." Econometric Theory 12, no. 2 (June 1996): 215–56. http://dx.doi.org/10.1017/s0266466600006575.

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In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.

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41

Arratia, Argimiro, Alejandra Cabaña, and Enrique M. Cabaña. "Embedding in law of discrete time ARMA processes in continuous time stationary processes." Journal of Statistical Planning and Inference 197 (December 2018): 156–67. http://dx.doi.org/10.1016/j.jspi.2018.01.004.

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42

van Noortwijk, J. M., and J. A. M. van der Weide. "Applications to continuous-time processes of computational techniques for discrete-time renewal processes." Reliability Engineering & System Safety 93, no. 12 (December 2008): 1853–60. http://dx.doi.org/10.1016/j.ress.2008.03.023.

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43

Stadje, Wolfgang. "FIRST-PASSAGE TIMES FOR SOME LINDLEY PROCESSES IN CONTINUOUS TIME." Sequential Analysis 21, no. 1-2 (May 20, 2002): 87–97. http://dx.doi.org/10.1081/sqa-120004174.

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44

Chazottes, Jean-René, Cristian Giardina, and Frank Redig. "Relative entropy and waiting times for continuous-time Markov processes." Electronic Journal of Probability 11 (2006): 1049–68. http://dx.doi.org/10.1214/ejp.v11-374.

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45

Cambanis, S., and E. Masry. "Performance of discrete-time predictors of continuous-time stationary processes." IEEE Transactions on Information Theory 34, no. 4 (July 1988): 655–68. http://dx.doi.org/10.1109/18.9766.

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46

Thornton, Michael A., and Marcus J. Chambers. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation." Journal of Economic Dynamics and Control 79 (June 2017): 48–65. http://dx.doi.org/10.1016/j.jedc.2017.03.012.

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47

Ma, Chunsheng. "Long-memory continuous-time correlation models." Journal of Applied Probability 40, no. 4 (September 2003): 1133–46. http://dx.doi.org/10.1239/jap/1067436105.

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This paper introduces a rather general class of stationary continuous-time processes with long memory by randomizing the time-scale of short-memory processes. In particular, by randomizing the time-scale of continuous-time autoregressive and moving-average processes, many power-law decay and slow decay correlation functions are obtained.

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48

Ma, Chunsheng. "Long-memory continuous-time correlation models." Journal of Applied Probability 40, no. 04 (December 2003): 1133–46. http://dx.doi.org/10.1017/s0021900200020349.

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This paper introduces a rather general class of stationary continuous-time processes with long memory by randomizing the time-scale of short-memory processes. In particular, by randomizing the time-scale of continuous-time autoregressive and moving-average processes, many power-law decay and slow decay correlation functions are obtained.

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49

Meyn, Sean P., and R. L. Tweedie. "Stability of Markovian processes II: continuous-time processes and sampled chains." Advances in Applied Probability 25, no. 3 (September 1993): 487–517. http://dx.doi.org/10.2307/1427521.

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In this paper we extend the results of Meyn and Tweedie (1992b) from discrete-time parameter to continuous-parameter Markovian processes Φ evolving on a topological space.We consider a number of stability concepts for such processes in terms of the topology of the space, and prove connections between these and standard probabilistic recurrence concepts. We show that these structural results hold for a major class of processes (processes with continuous components) in a manner analogous to discrete-time results, and that complex operations research models such as storage models with state-dependent release rules, or diffusion models such as those with hypoelliptic generators, have this property. Also analogous to discrete time, ‘petite sets', which are known to provide test sets for stability, are here also shown to provide conditions for continuous components to exist.New ergodic theorems for processes with irreducible and countably reducible skeleton chains are derived, and we show that when these conditions do not hold, then the process may be decomposed into an uncountable orbit of skeleton chains.

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50

Bartocci, Ezio, Luca Bortolussi, Tomáš Brázdil, Dimitrios Milios, and Guido Sanguinetti. "Policy learning in continuous-time Markov decision processes using Gaussian Processes." Performance Evaluation 116 (November 2017): 84–100. http://dx.doi.org/10.1016/j.peva.2017.08.007.

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