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Matematicheskie Trudy, 2015, Volume 18, Number 1, Pages 27–47
DOI: https://doi.org/10.17377/mattrudy.2015.18.103 (Mi mt285) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A “direct” method to prove the generalized Itô–Venttsel' formula for a generalized stochastic differential equation

E. V. Karachanskaya

Pacific National University, Khabarovsk, 680035, Russia
Full-text PDF (252 kB) Citations (2)
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DOI: https://doi.org/10.17377/mattrudy.2015.18.103
Abstract: For the first time we present a complete proof (from the standpoint of stochastic analysis) of the generalized Itô–Venttsel' formula whose ideas were adduced in [8]. The proposed proof is an approach to construct the generalized Itô–Venttsel' formula based on the direct application of the generalized Itô formula and the theory of stochastic approximation in contrast to the proof presented in [17] and based on the method of the integral invariants of a stochastic differential equation.
Key words: Itô–Venttsel' formula, generalized Itô equation, Poisson measure, $\delta$-sequence, mean-square convergence.
Received: 30.04.2014
English version:
Siberian Advances in Mathematics, 2016, Volume 26, Issue 1, Pages 17–29
DOI: https://doi.org/10.3103/S1055134416010028
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: E. V. Karachanskaya, “A “direct” method to prove the generalized Itô–Venttsel' formula for a generalized stochastic differential equation”, Mat. Tr., 18:1 (2015), 27–47; Siberian Adv. Math., 26:1 (2016), 17–29
Citation in format AMSBIB
\Bibitem{Kar15}
\by E.~V.~Karachanskaya
\paper A “direct” method to prove the generalized It\^o--Venttsel' formula for a generalized stochastic differential equation
\jour Mat. Tr.
\yr 2015
\vol 18
\issue 1
\pages 27--47
\mathnet{http://mi.mathnet.ru/mt285}
\crossref{https://doi.org/10.17377/mattrudy.2015.18.103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408634}
\elib{https://elibrary.ru/item.asp?id=23419033}
\transl
\jour Siberian Adv. Math.
\yr 2016
\vol 26
\issue 1
\pages 17--29
\crossref{https://doi.org/10.3103/S1055134416010028}
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