Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
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


Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 1, Pages 17–38 (Mi tvp790)  

Extrapolation of multidimensional Markov processes from incomplete data

R. Sh. Liptser, A. N. Shiryaev

Moscow

Abstract: Let $(\theta_t,\eta_t)$, $t\ge0$, be a Markov process, where $\eta_t$ is the observable component and $\theta_t$ is the unobservable one. Put
$$ \pi_\beta(\tau,t)=\mathbf P(\theta_\tau=\beta\mid\eta_s, s\le t),\quad\tau\ge t, $$
if $\theta_t$ takes discrete values and
$$ \pi_\beta(\tau,t)=\frac{\partial\mathbf P(\theta_t\le\beta\mid\eta_s, s\le t)}{\partial\beta},\quad\tau\ge t, $$
if $\theta_\tau$ takes continuous values. When $\theta_t$, $t\ge0$, is a purely discontinuous Markov process and $\eta_t$ has the stochastic differential (5), in § 1 equations in $t$ and $\tau$ for $\pi_\beta(\tau,t)$ are deduced. In § 2 equations for the density $\pi_\beta(\tau,t)$ are obtained under the supposition that $(\theta_t,\eta_t)$ be a diffusion Markov process. In § 3 some cases of effective solving of extrapolation problems for processes regarded in § 2 are considered.

Full text: PDF file (2978 kB)

English version:
Theory of Probability and its Applications, 1968, 13:1, 15–38

Bibliographic databases:

Received: 24.10.1967

Citation: R. Sh. Liptser, A. N. Shiryaev, “Extrapolation of multidimensional Markov processes from incomplete data”, Teor. Veroyatnost. i Primenen., 13:1 (1968), 17–38; Theory Probab. Appl., 13:1 (1968), 15–38

Citation in format AMSBIB
\Bibitem{LipShi68}
\by R.~Sh.~Liptser, A.~N.~Shiryaev
\paper Extrapolation of multidimensional Markov processes from incomplete data
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 1
\pages 17--38
\mathnet{http://mi.mathnet.ru/tvp790}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=235614}
\zmath{https://zbmath.org/?q=an:0245.60038}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 1
\pages 15--38
\crossref{https://doi.org/10.1137/1113002}


Linking options:
  • http://mi.mathnet.ru/eng/tvp790
  • http://mi.mathnet.ru/eng/tvp/v13/i1/p17

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:286
    Full text:108
    First page:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021