Geodesic
The generalized It\^o--Venttsel' formula in the case of a~noncentered Poisson measure, a~stochastic first integral, and a~first integral
Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 99-122

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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. 
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     author = {E. V. Karachanskaya},
     title = {The generalized {It\^o--Venttsel'} formula in the case of a~noncentered {Poisson} measure, a~stochastic first integral, and a~first integral},
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E. V. Karachanskaya. The generalized It\^o--Venttsel' formula in the case of a~noncentered Poisson measure, a~stochastic first integral, and a~first integral. Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 99-122. http://geodesic.mathdoc.fr/item/MT_2014_17_1_a3/