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, 1971, Volume 16, Issue 3, Pages 409–436 (Mi tvp2256)  

This article is cited in 8 scientific papers (total in 9 papers)

Wanderings of a Markov process

E. B. Dynkin

Moscow
Abstract: Let $X=(x_t,\zeta,M_t,\mathbf P_x)$ be a standard Markov process in a semi-compact $E$ and let $D$ be an open subset of the space $E$. The random set $\{t\colon x_t\in D\}$ consists of intervals $(\gamma,\delta)$ with the beginnings $\gamma$ of some of them. Wanderings of $X$ are the paths $\omega^\gamma$ in the space $D$ defined by the formula $w_t^\gamma=x_{\gamma+t}$ ($0<t<\delta-\gamma$).
For any left-continuous nonanticipating functional $F_t(\omega,w)$ ($t>0$, $\omega\in\Omega$, $w\in W$), we consider the sum of its values $F_\gamma(\omega,w^\gamma)$ over all wanderings of $X$ and we calculate the expectation of this sum in terms of an additive functional $\Phi$ of $X$ (the fundamental functional) and a kernel $b(x,\Gamma)$ (the entrance kernel). The main result is the formula of wanderings (1.8).
Received: 09.02.1970
English version:
Theory of Probability and its Applications, 1971, Volume 16, Issue 3, Pages 401–428
DOI: https://doi.org/10.1137/1116046
Bibliographic databases:
Language: Russian
Citation: E. B. Dynkin, “Wanderings of a Markov process”, Teor. Veroyatnost. i Primenen., 16:3 (1971), 409–436; Theory Probab. Appl., 16:3 (1971), 401–428
Citation in format AMSBIB
\Bibitem{Dyn71}
\by E.~B.~Dynkin
\paper Wanderings of a~Markov process
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 3
\pages 409--436
\mathnet{http://mi.mathnet.ru/tvp2256}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=293721}
\zmath{https://zbmath.org/?q=an:0272.60045}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 3
\pages 401--428
\crossref{https://doi.org/10.1137/1116046}
Linking options:
  • https://www.mathnet.ru/eng/tvp2256
  • https://www.mathnet.ru/eng/tvp/v16/i3/p409
  • This publication is cited in the following 9 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
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024