Integro-Differential Equations Generated by StochasticProblems

The connections between stochastic differential equations in which continuous and discontinuous random processes serve as sources of randomness and deterministic equations for the probabilistic characteristics of solutions of these stochastic equations are studied. In the study, we use various appro...

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Bibliographic Details
Published inDifferential equations Vol. 57; no. 3; pp. 379 - 390
Main Authors Melnikova, I V, Bovkun, V A, Alekseeva, U A
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.2021
Subjects
Differential equations
Formulas (mathematics)
Fourier transforms
Mathematical analysis
Mathematics
Operators (mathematics)
Probability theory
Random processes
Randomness
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Summary:The connections between stochastic differential equations in which continuous and discontinuous random processes serve as sources of randomness and deterministic equations for the probabilistic characteristics of solutions of these stochastic equations are studied. In the study, we use various approaches based on the stochastic change of variables formula (Itô’s formula), on the analysis of local infinitesimal characteristics of the process, and on the theory of semigroups of operators in combination with the generalized Fourier transform. This allows us to obtain direct and inverse integro-differential equations for various probabilistic characteristics.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266121030101