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arXiv · 1112.0621

On a generalization of the Itô-Wentzell formula for system of generalized Itô's SDE and the stochastic first integral

Elena V. Karachanskaya
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Abstract

Generalization of the Itô-Wentzell formula for the generalized Itô's SDE (Itô's GSDE) system with a non-centered measure is constructed on the basis of the stochastic kernel of integral transformation. The Itô's GSDE system for the kernel the solution of which is the kernel of the integral invariant, is formed. This invariant is connected with the solution of the Itô's GSDE system non-centered measure. The concept of a stochastic first integral of the Itô's GSDE system with non-centered measure is introduced and conditions that when being performed the random function is the first integral of the set Itô's GSDE system are defined.

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Elena V. Karachanskaya. 2011-12-03. On a generalization of the Itô-Wentzell formula for system of generalized Itô's SDE and the stochastic first integral. https://arxiv.org/abs/1112.0621

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