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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1982, Volume 27, Issue 3, Pages 425–433 (Mi tvp2376)

A comparison theorem for stochastic equations with integrals on martingales and random measures

L. I. Gal'čuk

Moscow

Abstract: We prove a comparison theorem for the solutions of general stochastic integral equations containing integrals on semimartingale's components. The equations with integrals on the Wiener process and the Poisson random measure are particular cases of the considered equations. It is proved that if the drift coefficient and the jump function for one equation are (in some sence) larger then for the other then the solution of the first equation is larger too.

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English version:
Theory of Probability and its Applications, 1983, 27:3, 450–460

Bibliographic databases:

Citation: L. I. Gal'čuk, “A comparison theorem for stochastic equations with integrals on martingales and random measures”, Teor. Veroyatnost. i Primenen., 27:3 (1982), 425–433; Theory Probab. Appl., 27:3 (1983), 450–460

Citation in format AMSBIB
\Bibitem{Gal82} \by L.~I.~Gal'{\v{c}}uk \paper A comparison theorem for stochastic equations with integrals on martingales and random measures \jour Teor. Veroyatnost. i Primenen. \yr 1982 \vol 27 \issue 3 \pages 425--433 \mathnet{http://mi.mathnet.ru/tvp2376} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=673916} \zmath{https://zbmath.org/?q=an:0516.60074} \transl \jour Theory Probab. Appl. \yr 1983 \vol 27 \issue 3 \pages 450--460 \crossref{https://doi.org/10.1137/1127055} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RJ51700002} 

• http://mi.mathnet.ru/eng/tvp2376
• http://mi.mathnet.ru/eng/tvp/v27/i3/p425

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. V. Melnikov, “Stochastic differential equations: singularity of coefficients, regression models, and stochastic approximation”, Russian Math. Surveys, 51:5 (1996), 819–909
2. A. S. Asylgareev, F. S. Nasyrov, “Theorems of comparison and stability with probability 1 for one-dimensional stochastic differential equations”, Siberian Math. J., 57:5 (2016), 754–761