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

2011/11/07 by Elena Karachanskaya, Karachanskaya, Elena V.
Computer Science · Economics, Econometrics and Finance · #60H15 (Primary) 58J70 (Secondary) #Complex Systems and Time Series Analysis #Cybersecurity and Information Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1111.1521

openalex publication_date 2011/11/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

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