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arXiv · 1111.1521

On a generalization of the It\^{o}-Wentzel formula for system of generalized It\^{o}'s SDEs and the stochastic first integral

Elena V. Karachanskaya
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Abstract

Generalization of the It\^{o}-Wentzel formula for the generalized It\^{o}'s SDEs (It\^{o}'s GSDEs) system with not centered measure is constructed. This construction is based on the basis of the stochastic kernel of integral transformation. The It\^{o}'s GSDEs system for the kernel of the integral invariant is constructed. The concept of a stochastic first integral of the It\^{o}'s GSDEs system with not centered measure is introduced. The conditions for the random function, that it's the first integral of the set It\^{o}'s GSDEs system, are defined.

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Elena V. Karachanskaya. 2011-11-07. On a generalization of the It\^{o}-Wentzel formula for system of generalized It\^{o}'s SDEs and the stochastic first integral. https://arxiv.org/abs/1111.1521

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