Email this article Stochastic differential equation in a random environment
- Authors: Makhno S.Y.1, Mel’nik S.A.1
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Affiliations:
- Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
- Issue: Vol 231, No 1 (2018)
- Pages: 48-69
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/241077
- DOI: https://doi.org/10.1007/s10958-018-3805-1
- ID: 241077
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Abstract
Solutions of the Itô stochastic differential equation in a random environment are considered. The random environment is formed by the generalized telegraph process. It is proved that the initial problem is equivalent to a system of two stochastic differential equations with nonrandom coefficients. The first equation is the Itô equation, and the initial process is its solution. The second equation is an equation with Poisson process, and its solution is a generalized telegraph process. The theorems of existence and uniqueness of strong and weak solutions are proved.
About the authors
Sergei Ya. Makhno
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
Author for correspondence.
Email: smahmo@gmail.com
Ukraine, Slavyansk
Sergei A. Mel’nik
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
Email: smahmo@gmail.com
Ukraine, Slavyansk
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