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This article is cited in 8 scientific papers (total in 9 papers)
The generalized Itô–Venttsel' formula in the case of a noncentered Poisson measure, a stochastic first integral, and a first integral
E. V. Karachanskaya Pacific National University, Khabarovsk, Russia
Abstract:
We deduce an analog of the Itô–Venttsel' formula for an Itô system of generalized stochastic differential equations (GSDE) with noncentered measure on the basis of a stochastic kernel of an integral invariant. We construct a system of GSDE whose solution is a kernel of an integral invariant connected with a solution to GSDE with noncentered measure. We introduce the notion of a stochastic first integral of a system of GSDE with noncentered measure and find conditions under which a random function is a first integral of a given system of GSDE.
Key words:
Itô–Venttsel' formula, generalized stochastic differential equation, noncentered Poisson measure, kernel of an integral invariant, stochastic first integral.
Received: 08.09.2013
Citation:
E. V. Karachanskaya, “The generalized Itô–Venttsel' formula in the case of a noncentered Poisson measure, a stochastic first integral, and a first integral”, Mat. Tr., 17:1 (2014), 99–122; Siberian Adv. Math., 25:3 (2015), 191–205
Linking options:
https://www.mathnet.ru/eng/mt268 https://www.mathnet.ru/eng/mt/v17/i1/p99
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Abstract page: | 507 | Full-text PDF : | 213 | References: | 54 | First page: | 21 |
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