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Stochastics Volume 3, 1980 - Issue 1-4
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Original Articles

Some limit theorems for simple point processes (a martingale approach)

YU. M. Kabanov Institute of Control Science, Moscow, USSRProfsoyuznaya 65
,
R. SH Liptser Institute of Control Science, Moscow, USSRProfsoyuznaya 65
&
A. N Shiryaev Steklov Mathematical Institute, Moscow, USSRVavilova 42
Pages 203-216 | Received 22 Aug 1979, Published online: 22 Dec 2010

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B. G. Ivanoff. (1989) Compensator approximations for point processes on the plane. Stochastics and Stochastic Reports 28:4, pages 317-341.
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ATA Al-Hussaini & J. elliott Robert. (1984) Convergence of the empirical distribution to the poisson process. Stochastics 13:4, pages 299-308.
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A. V. Mel'nikov. (1983) Stochastic equations and krylov's estimates for semimartingales. Stochastics 10:2, pages 81-102.
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A. V. Mel'nikov. (1982) On properties of strong solutions of stochastic equations with respect to semimartingales. Stochastics 8:2, pages 103-119.
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Esko Valkeila. (1982) A general poisson approximation theorem. Stochastics 7:3, pages 159-171.
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Articles from other publishers (20)

Eugene A. Feinberg, Pavlo O. Kasyanov & Michael Z. Zgurovsky. (2015) Convergence of probability measures and Markov decision models with incomplete information. Proceedings of the Steklov Institute of Mathematics 287:1, pages 96-117.
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Jean-Bernard Gravereaux & James Ledoux. (2016) Poisson approximation for some point processes in reliability. Advances in Applied Probability 36:2, pages 455-470.
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Jean-Bernard Gravereaux & James Ledoux. (2016) Poisson approximation for some point processes in reliability. Advances in Applied Probability 36:02, pages 455-470.
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A. G. Sholomitskii. (1999) On the Necessary Conditions of Normal Convergence for Martingales. Theory of Probability & Its Applications 43:3, pages 434-448.
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Aihua Xia. 1992. Séminaire de Probabilités XXVI. Séminaire de Probabilités XXVI 32 46 .
Yuji Kasahara & Keigo Yamada. (1991) Stability theorem for stochastic differential equations with jumps. Stochastic Processes and their Applications 38:1, pages 13-32.
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Martti Nikunen & Esko Valkeila. (1987) On the Levy-Prohorov distance between counting processes. Stochastic Processes and their Applications 26, pages 190.
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Jean Jacod. (1987) Sur la convergence des processus ponctuels. Probability Theory and Related Fields 76:4, pages 573-586.
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Fred B?ker. (1986) Convergence of thinning processes using compensators. Stochastic Processes and their Applications 23:1, pages 143-152.
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A. A. Grusho. (1986) On Convergence of Counting Processes Associated with U -Statistics . Theory of Probability & Its Applications 30:3, pages 626-630.
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Stewart N. Ethier & Thomas G. Kurtz. 1986. Markov Processes. Markov Processes 508 519 .
B. Gail Ivanoff. (2009) Poisson convergence for point processes on the plane. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 39:2, pages 253-269.
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M. Nikunen & E. Valkeila. (1985) A Note on One-Dimensional Distances between Two Counting Processes. Theory of Probability & Its Applications 29:3, pages 578-581.
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K. Kubilius. (1985) Necessary and sufficient conditions for the convergence of semimartingales to processes with conditionally independent increments. Lithuanian Mathematical Journal 24:2, pages 130-142.
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Yu. M. Kabanov, R. Sh. Liptser & A. N. Shiryaev. (1984) Weak and Strong Convergence of the Distributions of Counting Processes. Theory of Probability & Its Applications 28:2, pages 303-336.
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Yu. M. Kabanov & R. Sh. Liptser. (1983) On convergence in variation of the distributions of multivariate point processes. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete 63:4, pages 475-485.
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A. V. Melnikov. 1982. Stochastic Differential Systems. Stochastic Differential Systems 122 127 .
T. C. Brown. (2008) Compensators and Cox convergence. Mathematical Proceedings of the Cambridge Philosophical Society 90:2, pages 305-319.
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R. Sh. Liptser & A. N. Shiryayev. (1981) A Functional Central Limit Theorem for Semimartingales. Theory of Probability & Its Applications 25:4, pages 667-688.
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A. N. Shirayayev. (2016) Some limit theorems for simple point processes—martingale approach. Advances in Applied Probability 12:2, pages 278-279.
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