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Статті в журналах з теми "Shot-noise processes"

Автор: Grafiati

Опубліковано: 17 серпня 2022

Оновлено: 14 вересня 2022

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1

Møller, Jesper. "Shot noise Cox processes." Advances in Applied Probability 35, no. 03 (September 2003): 614–40. http://dx.doi.org/10.1017/s0001867800012465.

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Анотація:

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in ℝd, including Neyman-Scott, Poisson-gamma and shot noise G Cox processes. It is demonstrated that, due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function and local and spatial Markov properties.

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2

Møller, Jesper. "Shot noise Cox processes." Advances in Applied Probability 35, no. 3 (September 2003): 614–40. http://dx.doi.org/10.1239/aap/1059486821.

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Анотація:

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in ℝd, including Neyman-Scott, Poisson-gamma and shot noise G Cox processes. It is demonstrated that, due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function and local and spatial Markov properties.

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3

Møller, Jesper, and Giovanni Luca Torrisi. "Generalised shot noise Cox processes." Advances in Applied Probability 37, no. 01 (March 2005): 48–74. http://dx.doi.org/10.1017/s0001867800000033.

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Анотація:

We introduce a class of Cox cluster processes called generalised shot noise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process that drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby, a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and, second, on how to simulate such processes. In particular, results on first- and second-order moment measures, reduced Palm distributions, the J-function, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified in important special cases of GSNCPs, and we discuss their relation to the corresponding results for SNCPs.

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4

Møller, Jesper, and Giovanni Luca Torrisi. "Generalised shot noise Cox processes." Advances in Applied Probability 37, no. 1 (March 2005): 48–74. http://dx.doi.org/10.1239/aap/1113402399.

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Анотація:

We introduce a class of Cox cluster processes called generalised shot noise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process that drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby, a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and, second, on how to simulate such processes. In particular, results on first- and second-order moment measures, reduced Palm distributions, the J-function, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified in important special cases of GSNCPs, and we discuss their relation to the corresponding results for SNCPs.

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5

Hsing, Tailen, and J. L. Teugels. "Extremal properties of shot noise processes." Advances in Applied Probability 21, no. 03 (September 1989): 513–25. http://dx.doi.org/10.1017/s0001867800018784.

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Анотація:

Consider the shot noise process X(t):= Σi h(t – τ i ), , where h is a bounded positive non-increasing function supported on a finite interval, and the are the points of a renewal process η on [0, ). In this paper, the extremal properties of {X(t)} are studied. It is shown that these properties can be investigated in a natural way through a discrete-time process which records the states of {X(t)} at the points of η. The important special case where η is Poisson is treated in detail, and a domain-of-attraction result for the compound Poisson distribution is obtained as a by-product.

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6

Verovkin, G. K., and A. V. Marynych. "Stationary limits of shot noise processes." Theory of Probability and Mathematical Statistics 101 (January 5, 2021): 67–83. http://dx.doi.org/10.1090/tpms/1112.

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7

Hsing, Tailen, and J. L. Teugels. "Extremal properties of shot noise processes." Advances in Applied Probability 21, no. 3 (September 1989): 513–25. http://dx.doi.org/10.2307/1427633.

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Анотація:

Consider the shot noise process X(t):= Σih(t – τi), , where h is a bounded positive non-increasing function supported on a finite interval, and the are the points of a renewal process η on [0, ). In this paper, the extremal properties of {X(t)} are studied. It is shown that these properties can be investigated in a natural way through a discrete-time process which records the states of {X(t)} at the points of η. The important special case where η is Poisson is treated in detail, and a domain-of-attraction result for the compound Poisson distribution is obtained as a by-product.

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8

Biermé, Hermine, and Agnès Desolneux. "Crossings of smooth shot noise processes." Annals of Applied Probability 22, no. 6 (December 2012): 2240–81. http://dx.doi.org/10.1214/11-aap807.

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9

Miyoshi, Naoto. "CORRECTION TO “A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES”." Probability in the Engineering and Informational Sciences 19, no. 3 (June 22, 2005): 405–7. http://dx.doi.org/10.1017/s0269964805050242.

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Анотація:

In the Note published last year [1], bounds and monotonicity of shot-noise and max-shot-noise processes driven by spatial stationary Cox point processes are discussed in terms of some stochastic order. Although all the statements concerning the shot-noise processes remain valid, those concerning the max-shot-noise processes have to be corrected.

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10

Iksanov, Alexander, and Bohdan Rashytov. "A functional limit theorem for general shot noise processes." Journal of Applied Probability 57, no. 1 (March 2020): 280–94. http://dx.doi.org/10.1017/jpr.2019.95.

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Анотація:

AbstractBy a general shot noise process we mean a shot noise process in which the counting process of shots is arbitrary locally finite. Assuming that the counting process of shots satisfies a functional limit theorem in the Skorokhod space with a locally Hölder continuous Gaussian limit process, and that the response function is regularly varying at infinity, we prove that the corresponding general shot noise process satisfies a similar functional limit theorem with a different limit process and different normalization and centering functions. For instance, if the limit process for the counting process of shots is a Brownian motion, then the limit process for the general shot noise process is a Riemann–Liouville process. We specialize our result for five particular counting processes. Also, we investigate Hölder continuity of the limit processes for general shot noise processes.

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11

Lund, Robert, William P. McCormick, and Yuanhui Xiao. "Limiting properties of Poisson shot noise processes." Journal of Applied Probability 41, no. 03 (September 2004): 911–18. http://dx.doi.org/10.1017/s0021900200020623.

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Анотація:

This paper studies limiting properties of discretely sampled Poisson shot noise processes. Versions of the law of large numbers and central limit theorem are derived under very general conditions. Examples demonstrating the utility of the results are included.

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12

Schmidt, Thorsten. "Catastrophe Insurance Modeled by Shot-Noise Processes." Risks 2, no. 1 (February 21, 2014): 3–24. http://dx.doi.org/10.3390/risks2010003.

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13

Lund, Robert, William P. McCormick, and Yuanhui Xiao. "Limiting properties of Poisson shot noise processes." Journal of Applied Probability 41, no. 3 (September 2004): 911–18. http://dx.doi.org/10.1239/jap/1091543433.

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Анотація:

This paper studies limiting properties of discretely sampled Poisson shot noise processes. Versions of the law of large numbers and central limit theorem are derived under very general conditions. Examples demonstrating the utility of the results are included.

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14

Brix, Anders. "Generalized Gamma measures and shot-noise Cox processes." Advances in Applied Probability 31, no. 04 (December 1999): 929–53. http://dx.doi.org/10.1017/s0001867800009538.

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Анотація:

A parametric family of completely random measures, which includes gamma random measures, positive stable random measures as well as inverse Gaussian measures, is defined. In order to develop models for clustered point patterns with dependencies between points, the family is used in a shot-noise construction as intensity measures for Cox processes. The resulting Cox processes are of Poisson cluster process type and include Poisson processes and ordinary Neyman-Scott processes. We show characteristics of the completely random measures, illustrated by simulations, and derive moment and mixing properties for the shot-noise random measures. Finally statistical inference for shot-noise Cox processes is considered and some results on nearest-neighbour Markov properties are given.

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15

Brix, Anders. "Generalized Gamma measures and shot-noise Cox processes." Advances in Applied Probability 31, no. 4 (December 1999): 929–53. http://dx.doi.org/10.1239/aap/1029955251.

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Анотація:

A parametric family of completely random measures, which includes gamma random measures, positive stable random measures as well as inverse Gaussian measures, is defined. In order to develop models for clustered point patterns with dependencies between points, the family is used in a shot-noise construction as intensity measures for Cox processes. The resulting Cox processes are of Poisson cluster process type and include Poisson processes and ordinary Neyman-Scott processes.We show characteristics of the completely random measures, illustrated by simulations, and derive moment and mixing properties for the shot-noise random measures. Finally statistical inference for shot-noise Cox processes is considered and some results on nearest-neighbour Markov properties are given.

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16

Budhiraja, Amarjit, and Pierre Nyquist. "Large deviations for multidimensional state-dependent shot-noise processes." Journal of Applied Probability 52, no. 04 (December 2015): 1097–114. http://dx.doi.org/10.1017/s0021900200113105.

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Анотація:

Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

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17

Budhiraja, Amarjit, and Pierre Nyquist. "Large deviations for multidimensional state-dependent shot-noise processes." Journal of Applied Probability 52, no. 4 (December 2015): 1097–114. http://dx.doi.org/10.1239/jap/1450802755.

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Анотація:

Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

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18

Hellmund, Gunnar, Michaela Prokešová, and Eva B. Vedel Jensen. "Lévy-based Cox point processes." Advances in Applied Probability 40, no. 03 (September 2008): 603–29. http://dx.doi.org/10.1017/s0001867800002718.

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Анотація:

In this paper we introduce Lévy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function Λ defined by a kernel smoothing of a Lévy basis (an independently scattered, infinitely divisible random measure). We also consider log Lévy-driven Cox point processes (LLCPs) with Λ equal to the exponential of such a kernel smoothing. Special cases are shot noise Cox processes, log Gaussian Cox processes, and log shot noise Cox processes. We study the theoretical properties of Lévy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.

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19

Hellmund, Gunnar, Michaela Prokešová, and Eva B. Vedel Jensen. "Lévy-based Cox point processes." Advances in Applied Probability 40, no. 3 (September 2008): 603–29. http://dx.doi.org/10.1239/aap/1222868178.

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Анотація:

In this paper we introduce Lévy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function Λ defined by a kernel smoothing of a Lévy basis (an independently scattered, infinitely divisible random measure). We also consider log Lévy-driven Cox point processes (LLCPs) with Λ equal to the exponential of such a kernel smoothing. Special cases are shot noise Cox processes, log Gaussian Cox processes, and log shot noise Cox processes. We study the theoretical properties of Lévy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.

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20

Chobanov, G. "Modeling financial asset returns with shot noise processes." Mathematical and Computer Modelling 29, no. 10-12 (May 1999): 17–21. http://dx.doi.org/10.1016/s0895-7177(99)00089-8.

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21

Gregori, P., M. N. M. van Lieshout, and J. Mateu. "Mixture formulae for shot noise weighted point processes." Statistics & Probability Letters 67, no. 4 (May 2004): 311–20. http://dx.doi.org/10.1016/j.spl.2004.02.003.

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22

Schmidt, V. "On finiteness and continuity of shot noise processes." Optimization 16, no. 6 (January 1985): 921–33. http://dx.doi.org/10.1080/02331938508843094.

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23

Schmidt, Thorsten, and Winfried Stute. "Shot-noise processes and the minimal martingale measure." Statistics & Probability Letters 77, no. 12 (July 2007): 1332–38. http://dx.doi.org/10.1016/j.spl.2007.03.019.

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24

Schmidt, Volkeb. "Poisson bounds for moments of shot noise processes." Statistics 16, no. 2 (January 1985): 253–62. http://dx.doi.org/10.1080/02331888508801853.

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25

Ramirez-Perez, Filemon, and Robert Serfling. "Shot noise on cluster processes with cluster marks, and studies of long range dependence." Advances in Applied Probability 33, no. 03 (September 2001): 631–51. http://dx.doi.org/10.1017/s0001867800011046.

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Анотація:

With the aim of providing greater flexibility in developing and applying shot noise models, this paper studies shot noise on cluster point processes with both pointwise and cluster marks. For example, in financial modelling, responses to events in the financial market may occur in clusters, with random amplitudes including a ‘cluster component’ reflecting a degree of commonness among responses within a cluster. For such shot noise models, general formulae for the characteristic functional are developed and specialized to the case of Neyman-Scott clustering with cluster marks. For several general forms of response function, long range dependence of the corresponding equilibrium shot noise models is investigated. It is shown, for example, that long range dependence holds when the ‘structure component’ of the response function decays slowly enough, or when the response function has a finite random duration with a heavy tailed distribution.

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26

Ramirez-Perez, Filemon, and Robert Serfling. "Shot noise on cluster processes with cluster marks, and studies of long range dependence." Advances in Applied Probability 33, no. 3 (September 2001): 631–51. http://dx.doi.org/10.1239/aap/1005091357.

Повний текст джерела

Анотація:

With the aim of providing greater flexibility in developing and applying shot noise models, this paper studies shot noise on cluster point processes with both pointwise and cluster marks. For example, in financial modelling, responses to events in the financial market may occur in clusters, with random amplitudes including a ‘cluster component’ reflecting a degree of commonness among responses within a cluster. For such shot noise models, general formulae for the characteristic functional are developed and specialized to the case of Neyman-Scott clustering with cluster marks. For several general forms of response function, long range dependence of the corresponding equilibrium shot noise models is investigated. It is shown, for example, that long range dependence holds when the ‘structure component’ of the response function decays slowly enough, or when the response function has a finite random duration with a heavy tailed distribution.

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27

Miyoshi, Naoto. "A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES." Probability in the Engineering and Informational Sciences 18, no. 4 (October 2004): 561–71. http://dx.doi.org/10.1017/s026996480418409x.

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Анотація:

We consider shot-noise and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive their upper and lower bounds in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processes, we show the monotonicity result which implies that more variable shot patterns lead to more variable shot noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queuing theory.

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28

Dassios, Angelos, and Jiwook Jang. "The Distribution of the Interval between Events of a Cox Process with Shot Noise Intensity." Journal of Applied Mathematics and Stochastic Analysis 2008 (November 25, 2008): 1–14. http://dx.doi.org/10.1155/2008/367170.

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Анотація:

Applying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance.

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29

van Lieshout, M. N. M., and I. S. Molchanov. "Shot noise weighted processes: a new family of spatial point processes." Communications in Statistics. Stochastic Models 14, no. 3 (January 1998): 715–34. http://dx.doi.org/10.1080/15326349808807496.

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30

McCormick, William P. "Extremes for shot noise processes with heavy tailed amplitudes." Journal of Applied Probability 34, no. 3 (September 1997): 643–56. http://dx.doi.org/10.2307/3215091.

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Анотація:

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k} are the points of a renewal process and {Ak} are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

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31

Prokešová, Michaela, and Jiří Dvořák. "Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes." Methodology and Computing in Applied Probability 16, no. 2 (March 1, 2013): 433–49. http://dx.doi.org/10.1007/s11009-013-9324-0.

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32

McCormick, William P. "Extremes for shot noise processes with heavy tailed amplitudes." Journal of Applied Probability 34, no. 03 (September 1997): 643–56. http://dx.doi.org/10.1017/s0021900200101317.

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Анотація:

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k } are the points of a renewal process and {Ak } are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

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33

Petracchi, D., G. Cercignani, and S. Lucia. "Photoreceptor sensitivity and the shot noise of chemical processes." Biophysical Journal 70, no. 1 (January 1996): 111–20. http://dx.doi.org/10.1016/s0006-3495(96)79553-x.

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34

Masoliver, Jaume. "First-passage times for non-Markovian processes: Shot noise." Physical Review A 35, no. 9 (May 1, 1987): 3918–28. http://dx.doi.org/10.1103/physreva.35.3918.

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35

Jang, Jiwook, Angelos Dassios, and Hongbiao Zhao. "Moments of renewal shot-noise processes and their applications." Scandinavian Actuarial Journal 2018, no. 8 (March 20, 2018): 727–52. http://dx.doi.org/10.1080/03461238.2018.1452285.

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36

Masoliver, Jaume, and George H. Weiss. "Some first passage time problems for shot noise processes." Journal of Statistical Physics 50, no. 1-2 (January 1988): 377–82. http://dx.doi.org/10.1007/bf01022999.

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37

Dong, Yinghui, Kam C. Yuen, and Chongfeng Wu. "Regime-switching shot-noise processes and longevity bond pricing." Lithuanian Mathematical Journal 54, no. 4 (October 2014): 383–402. http://dx.doi.org/10.1007/s10986-014-9251-y.

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38

Torrisi, Giovanni Luca, and Emilio Leonardi. "Asymptotic analysis of Poisson shot noise processes, and applications." Stochastic Processes and their Applications 144 (February 2022): 229–70. http://dx.doi.org/10.1016/j.spa.2021.11.008.

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39

Biermé, Hermine, and Agnès Desolneux. "A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps." Journal of Applied Probability 49, no. 01 (March 2012): 100–113. http://dx.doi.org/10.1017/s0021900200008883.

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Анотація:

We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

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40

Biermé, Hermine, and Agnès Desolneux. "A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps." Journal of Applied Probability 49, no. 1 (March 2012): 100–113. http://dx.doi.org/10.1239/jap/1331216836.

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Анотація:

We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

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41

Pang, Guodong, and Yuhang Zhou. "Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises." Stochastic Systems 10, no. 2 (June 2020): 99–123. http://dx.doi.org/10.1287/stsy.2019.0051.

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We study shot noise processes when the shot noises are weakly dependent, satisfying the ρ-mixing condition. We prove a functional weak law of large numbers and a functional central limit theorem for this shot noise process in an asymptotic regime with a high intensity of shots. The deterministic fluid limit is unaffected by the presence of weak dependence. The limit in the diffusion scale is a continuous Gaussian process whose covariance function explicitly captures the dependence among the noises. The model and results can be applied in financial and insurance risks with dependent claims as well as queueing systems with dependent service times. To prove the existence of the limit process, we employ the existence criterion that uses a maximal inequality requiring a set function with a superadditivity property. We identify such a set function for the limit process by exploiting the ρ-mixing condition. To prove the weak convergence, we establish the tightness property and the convergence of finite dimensional distributions. To prove tightness, we construct two auxiliary processes and apply an Ottaviani-type inequality for weakly dependent sequences.

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42

Klüppelberg, Claudia, Thomas Mikosch, and Claudia Kluppelberg. "Explosive Poisson Shot Noise Processes with Applications to Risk Reserves." Bernoulli 1, no. 1/2 (March 1995): 125. http://dx.doi.org/10.2307/3318683.

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43

Liese, Friedrich, and Volker Schmidt. "Asymptotic properties of intensity estimators for Poisson shot-noise processes." Journal of Applied Probability 28, no. 3 (September 1991): 568–83. http://dx.doi.org/10.2307/3214492.

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Stochastic processes {X(t)} of the form X(t) = Σ n f(t – Tn) are considered, where {Tn} is a stationary Poisson point process with intensity λ and f: R → R is an unknown response function. Conditions are obtained for weak consistency and asymptotic normality of estimators of λ based on long-run observations of {X(t)}.

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44

Prokešová, Michaela, Jiří Dvořák, and Eva B. Vedel Jensen. "Two-step estimation procedures for inhomogeneous shot-noise Cox processes." Annals of the Institute of Statistical Mathematics 69, no. 3 (February 27, 2016): 513–42. http://dx.doi.org/10.1007/s10463-016-0556-y.

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45

Liese, Friedrich, and Volker Schmidt. "Asymptotic properties of intensity estimators for Poisson shot-noise processes." Journal of Applied Probability 28, no. 03 (September 1991): 568–83. http://dx.doi.org/10.1017/s002190020004242x.

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Анотація:

Stochastic processes {X(t)} of the form X(t) = Σ n f(t – Tn ) are considered, where {Tn } is a stationary Poisson point process with intensity λ and f: R → R is an unknown response function. Conditions are obtained for weak consistency and asymptotic normality of estimators of λ based on long-run observations of {X(t)}.

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46

Vasylyk, O. I. "Properties of strictly $\varphi $-sub-Gaussian quasi-shot-noise processes." Theory of Probability and Mathematical Statistics 101 (January 5, 2021): 51–65. http://dx.doi.org/10.1090/tpms/1111.

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47

Heinrich, L., and I. S. Molchanov. "Some Limit Theorems for Extremal and Union Shot-Noise Processes." Mathematische Nachrichten 168, no. 1 (November 11, 2006): 139–59. http://dx.doi.org/10.1002/mana.19941680109.

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48

Leonardi, Emilio, and Giovanni Luca Torrisi. "Modeling LEAST RECENTLY USED caches with Shot Noise request processes." SIAM Journal on Applied Mathematics 77, no. 2 (January 2017): 361–83. http://dx.doi.org/10.1137/15m1041444.

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49

Cheng, Zailei, and Youngsoo Seol. "Precise deviations for Cox processes with a shot noise intensity." Communications in Statistics - Theory and Methods 48, no. 23 (December 29, 2018): 5850–61. http://dx.doi.org/10.1080/03610926.2018.1522351.

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50

Lane, John A. "The Berry-Esseen bound for the Poisson shot-noise." Advances in Applied Probability 19, no. 02 (June 1987): 512–14. http://dx.doi.org/10.1017/s0001867800016670.

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This note provides a useful extension of the Berry–Esseen bound on the error in the normal approximation for shot-noise. The special cases treated are of particular interest in the statistical analysis of Poisson processes and cluster point processes.

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