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, 2008, Volume 53, Issue 2, Pages 213–239
DOI: https://doi.org/10.4213/tvp1725
(Mi tvp1725)
 

This article is cited in 16 scientific papers (total in 16 papers)

Positive Densities of Transition Probabilities of Diffusion Processes

V. I. Bogacheva, M. Röcknerb, S. V. Shaposhnikovc

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Bielefeld University
c M. V. Lomonosov Moscow State University
References:
Abstract: For diffusion processes in $\mathbf R^d$ with locally unbounded drift coefficients we obtain a sufficient condition for the strict positivity of transition probabilities. To this end, we consider parabolic equations of the form $\mathcal L^*\mu=0$ with respect to measures on $\mathbf R^d\times (0,1)$ with the operator $\mathcal L u:=\partial_t u+\partial_{x_i}(a^{ij}\partial_{x_j}u)+b^i\partial_{x_i}u$. It is shown that if the diffusion coefficient $A=(a^{ij})$ is sufficiently regular and the drift coefficient $b=(b^i)$ satisfies the condition $\exp(\kappa |b|^2)\in L_{\mathrm{loc}}^1(\mu)$, where the measure $\mu$ is nonnegative, then $\mu$ has a continuous density $\varrho(x,t)$ which is strictly positive for $t>\tau$ provided that it is not identically zero for $t\le\tau$. Applications are obtained to finite-dimensional projections of stationary distributions and transition probabilities of infinite-dimensional diffusions.
Keywords: density of transition probability, stationary distribution, parabolic equation, infinite-dimensional diffusion.
Received: 26.11.2007
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 2, Pages 194–215
DOI: https://doi.org/10.1137/S0040585X97983523
Bibliographic databases:
Language: Russian
Citation: V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Positive Densities of Transition Probabilities of Diffusion Processes”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 213–239; Theory Probab. Appl., 53:2 (2009), 194–215
Citation in format AMSBIB
\Bibitem{BogRocSha08}
\by V.~I.~Bogachev, M.~R\"ockner, S.~V.~Shaposhnikov
\paper Positive Densities of Transition Probabilities of Diffusion Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 2
\pages 213--239
\mathnet{http://mi.mathnet.ru/tvp1725}
\crossref{https://doi.org/10.4213/tvp1725}
\elib{https://elibrary.ru/item.asp?id=13601573}
\transl
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 2
\pages 194--215
\crossref{https://doi.org/10.1137/S0040585X97983523}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267617600002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67249131117}
Linking options:
  • https://www.mathnet.ru/eng/tvp1725
  • https://doi.org/10.4213/tvp1725
  • https://www.mathnet.ru/eng/tvp/v53/i2/p213
  • This publication is cited in the following 16 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:779
    Full-text PDF :211
    References:100
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024