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Mat. Tr., 2017, Volume 20, Number 1, Pages 128–144 (Mi mt318)  

Stochastic equations with discontinuous jump functions

A. V. Logachovabc, S. Ya. Makhnod

a Novosibirsk State University of Economics and Management, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Siberian State University of Geosystems and Technologies, Novosibirsk, Russia
d Institute of Applied Mathematics and Mechanics, Slavyansk, Ukraine

Abstract: In the present article, we consider a stochastic differential equation that contains an integral with respect to a Poisson measure but avoids the diffusion term. The integrand need not be continuous. We introduce a definition of a solution and prove the existence and uniqueness theorems.

Key words: stochastic differential equation, Poisson measure, differential inclusions.

DOI: https://doi.org/10.17377/mattrudy.2017.20.108

Full text: PDF file (243 kB)
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English version:
Siberian Advances in Mathematics, 2017, 27:4, 263–273

Document Type: Article
UDC: 519.2
Received: 17.05.2016

Citation: A. V. Logachov, S. Ya. Makhno, “Stochastic equations with discontinuous jump functions”, Mat. Tr., 20:1 (2017), 128–144; Siberian Adv. Math., 27:4 (2017), 263–273

Citation in format AMSBIB
\Bibitem{LogMak17}
\by A.~V.~Logachov, S.~Ya.~Makhno
\paper Stochastic equations with discontinuous jump functions
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 1
\pages 128--144
\mathnet{http://mi.mathnet.ru/mt318}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.108}
\elib{http://elibrary.ru/item.asp?id=29145406}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 4
\pages 263--273
\crossref{https://doi.org/10.3103/S1055134417040046}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85036518815}


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