Invariance principle for one class of Markov chains with fast Poisson time. Estimate for the rate of convergence
- 21 Downloads
We obtain an estimate for the rate of convergence of normalized Poisson sums of random variables determined by the first-order autoregression procedure to a family of Wiener processes.
KeywordsPoisson Process Independent Random Variable Wiener Process Invariance Principle Discrete Analog
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 2.S. V. Anulova, A. Yu. Veretennikov, N. V. Krylov, R. Sh. Liptser, and A. N. Shiryaev, “Stochastic calculus,” in: VINITI Series in Contemporary Problems of Mathematics [in Russian], Vol. 45, VINITI, Moscow (1989), pp. 5–257.Google Scholar
- 4.A. V. Baev and B. V. Bondarev, “Invariance principle for one class of stationary Markov processes. Estimate for the rate of convergence,” Visn. Donets’kogo Univ., Ser. A, Pryrod. Nauky, Issue 2, 7–17 (2002).Google Scholar
- 6.A. I. Sakhanenko, “Rate of convergence in the invariance principle for differently distributed variables with exponential moments,” in: Limit Theorems for Sums of Random Variables [in Russian], Nauka, Novosibirsk (1984), pp. 4–50.Google Scholar
- 8.B. V. Bondarev and A. A. Kolosov, “An approximation in probability of normalized integrals of processes with weak dependence by a set of Wiener processes and its applications,” Prikl. Statist. Aktuar. Finans. Mat., No. 2, 39–65 (2000).Google Scholar
- 9.B. V. Bondarev, A. V. Baev, and O. S. Khudalii, “Some problems for a compound Poisson process,” Prikl. Statist. Aktuar. Finans. Mat., No. 1, 3–15 (2004).Google Scholar
- 10.A. Yu. Zaitsev, On the Gaussian Approximation of Convolutions in the Case of Validity of Multidimensional Analogs of the Bernshtein Inequality [in Russian], Preprint No. P-9-84, Leningrad Division of the Mathematical Institute of the Academy of Sciences of the USSR, Leningrad (1984).Google Scholar
- 12.B. V. Bondarev, Mathematical Models in Insurance [in Russian], Apeks, Donetsk (2003).Google Scholar
- 13.A. V. Skorokhod, Lectures on Random Processes [in Ukrainian], Lybid’, Kyiv (1990).Google Scholar
- 14.I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).Google Scholar
- 17.B. V. Bondarev, “Bernshtein inequality for the estimation of the parameter of first-order autoregression,” Teor. Imov. Mat. Statist., Issue 55, 13–19 (1996).Google Scholar
- 18.R. Sh. Liptser and A. N. Shiryaev, Statistics of Random Processes [in Russian], Nauka, Moscow (1974).Google Scholar
© Springer Science+Business Media, Inc. 2006