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

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

2011-12-03

arxiv.org/abs/1112.0621v1

Mathematics

Probability

21 pages, English variant, translated from Russian

Scientific paper

Generalization of the It\^{o}-Wentzell formula for the generalized It\^{o}'s SDE (It\^{o}'s GSDE) system with a non-centered measure is constructed on the basis of the stochastic kernel of integral transformation. The It\^{o}'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 It\^{o}'s GSDE system non-centered measure. The concept of a stochastic first integral of the It\^{o}'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 It\^{o}'s GSDE system are defined.

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