Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 3, Pages 512–526 (Mi tvp3396)  

This article is cited in 20 scientific papers (total in 20 papers)

Rough limit theorems on large deviations for Markov stochastic processes. II

A. D. Wentzell

Moscow
Abstract: The first part of this paper was published in vol. XXI, No. 2 (1976) of this journal.
In the second part we deal not with Markov processes but rather with their characteristics. The results of § 5 are used to establish properties of the standardized action functional and the relation between it and the action functional. In § 7 we verify, in some natural cases, a somewhat intricate continuity condition imposed on the characteristics of the Markov processes under consideration.
In § 6 we introduce two classes (discrete-time and continuous-time) of families of Markov processes, and we prove our main results. Markov processes $\xi^{\alpha}(t)$ of these families have jumps becoming smaller and smaller as $\alpha$ increases but more and more frequent (and the diffusion parts of the processes are changing in accordance with the jumps). The most close to our results are those of [2] (concerning processes with independent increments) and [3] (concerning diffusion processes). Our results are valid for a wider class of families of Markov processes which includes both families of processes with independent increments and of diffusion processes with small diffusion.
The results of the present paper are analogous to limit theorems on large deviations for sums of independent random variables concerning «very large» deviations of order $\sqrt n$ (for precise results for sums of independent random variables see [1], Theorem 6). The case, analogous to that of «not very large» deviations (of order $o(\sqrt n)$ see [1], Theorem 1), will be considered in another paper.
Received: 08.10.1974
English version:
Theory of Probability and its Applications, 1977, Volume 21, Issue 3, Pages 499–512
DOI: https://doi.org/10.1137/1121062
Bibliographic databases:
Language: Russian
Citation: A. D. Wentzell, “Rough limit theorems on large deviations for Markov stochastic processes. II”, Teor. Veroyatnost. i Primenen., 21:3 (1976), 512–526; Theory Probab. Appl., 21:3 (1977), 499–512
Citation in format AMSBIB
\Bibitem{Ven76}
\by A.~D.~Wentzell
\paper Rough limit theorems on large deviations for Markov stochastic processes.~II
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 3
\pages 512--526
\mathnet{http://mi.mathnet.ru/tvp3396}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=433566}
\zmath{https://zbmath.org/?q=an:0361.60006}
\transl
\jour Theory Probab. Appl.
\yr 1977
\vol 21
\issue 3
\pages 499--512
\crossref{https://doi.org/10.1137/1121062}
Linking options:
  • https://www.mathnet.ru/eng/tvp3396
  • https://www.mathnet.ru/eng/tvp/v21/i3/p512
    Cycle of papers
    This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
    Statistics & downloads:
    Abstract page:296
    Full-text PDF :125
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024