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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 4, Pages 685–701 (Mi tvp3500)  

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

On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions

A. Ju. Veretennikov

Moscow

Abstract: We investigate the sufficient conditions for the strong and weak uniqueness of the solution of a stochastic equation with a simultaneous reflection at zero:
\begin{gather*} dx_s=\sigma(s,x_s) dw_s+b(s,x_s) ds+d\varphi_s,
d\varphi_s=\chi_{x_s=0} d\varphi_s,\qquad x_s\ge 0, \end{gather*}
and for the existence of a strong solution of this equation.

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English version:
Theory of Probability and its Applications, 1982, 26:4, 670–686

Bibliographic databases:

Received: 16.05.1979

Citation: A. Ju. Veretennikov, “On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 685–701; Theory Probab. Appl., 26:4 (1982), 670–686

Citation in format AMSBIB
\Bibitem{Ver81}
\by A.~Ju.~Veretennikov
\paper On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 685--701
\mathnet{http://mi.mathnet.ru/tvp3500}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=636765}
\zmath{https://zbmath.org/?q=an:0499.60064}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 670--686
\crossref{https://doi.org/10.1137/1126076}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PM42700002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Veretennikov A.Y., “On lower bounds for mixing coefficients of Markov diffusions”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 623–633  isi
    2. O. A. Manita, A. Yu. Veretennikov, “O skhodimosti odnomernoi markovskoi diffuzii k statsionarnoi plotnosti s tyazhelymi khvostami”, Mosc. Math. J., 19:1 (2019), 89–106  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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