Approximate solutions for fuzzy stochastic differential equations with Markovian switching

The fuzzy stochastic differential equations with Markovian switching are considered. First, under the [Formula: see text] assumptions, the existence and uniqueness theorem for the aforementioned equations is given by means of stopping time techniques, discretization method, and the Gronwall-Bellman...

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Bibliographic Details
Published in:Applied mathematics in science and engineering 2024-12, Vol.32 (1)
Main Authors: Wang, Peiguang, Li, Beibei
Format: Article
Language:English
Subjects:
65C30
averaging method
Bihari's inequality
existence and uniqueness
Fuzzy stochastic differential equations
fuzzy stochastic processes
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Summary:The fuzzy stochastic differential equations with Markovian switching are considered. First, under the [Formula: see text] assumptions, the existence and uniqueness theorem for the aforementioned equations is given by means of stopping time techniques, discretization method, and the Gronwall-Bellman inequality. Then the boundedness of the second moment of the solutions for such equations is established. Furthermore, by using the averaging method and stochastic analysis, as well as the Bihari's inequality, this paper mainly demonstrates the asymptotic relationship between the solutions of the original equations and the corresponding averaged equations in terms of mean square and probability. Finally, the theoretical result of the averaging method is illustrated by an example.
ISSN:2769-0911
2769-0911
DOI:10.1080/27690911.2024.2331147