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, 1984, Volume 29, Issue 1, Pages 120–123 (Mi tvp1966)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the existence of a strong solution of an Ito stochastic differential equation

I. V. Fedorenko

Krasnodar
Full-text PDF (277 kB) Citations (2)
Abstract: It is shown that the scalar stochastic differential equation
$$ x_t=x_0+\int_0^t A(s,x_s)\,ds+\int_0^t B(s,x_s)\,dw_s,\qquad 0\le t\le T, $$
has at least one strong solution under the following conditions:
a) scalar functions $A(t,x)$ and $B(t,x)$ are continuous in both $t$, $x$ for $0\le t\le T$, $-\infty<x<\infty$;
b) $B(t,x)$ satisfies a local Lipschitz conditions in $x$;
c) $|A(t,x)|+ |B(t,x)|\le L(1+|x|)$ for some constant $L$ and all $t$, $x$;
d) $\mathbf Mx_0^2<\infty$.
Received: 06.07.1981
English version:
Theory of Probability and its Applications, 1985, Volume 29, Issue 1, Pages 121–123
DOI: https://doi.org/10.1137/1129012
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. V. Fedorenko, “On the existence of a strong solution of an Ito stochastic differential equation”, Teor. Veroyatnost. i Primenen., 29:1 (1984), 120–123; Theory Probab. Appl., 29:1 (1985), 121–123
Citation in format AMSBIB
\Bibitem{Fed84}
\by I.~V.~Fedorenko
\paper On the existence of a~strong solution of an Ito stochastic differential equation
\jour Teor. Veroyatnost. i Primenen.
\yr 1984
\vol 29
\issue 1
\pages 120--123
\mathnet{http://mi.mathnet.ru/tvp1966}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=739507}
\zmath{https://zbmath.org/?q=an:0555.60035|0525.60066}
\transl
\jour Theory Probab. Appl.
\yr 1985
\vol 29
\issue 1
\pages 121--123
\crossref{https://doi.org/10.1137/1129012}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1985AFG0600012}
Linking options:
  • https://www.mathnet.ru/eng/tvp1966
  • https://www.mathnet.ru/eng/tvp/v29/i1/p120
  • This publication is cited in the following 2 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