Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients

The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler–Maruyama scheme associated with the consequent weakly i...

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Bibliographic Details
Published inJournal of theoretical probability Vol. 35; no. 2; pp. 1187 - 1215
Main Authors Bao, Jianhai, Huang, Xing
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2022
Springer Nature B.V
Subjects
Differential equations
Freezing
Mathematical analysis
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
65C30
65C35
McKean–Vlasov stochastic differential equation
Zvonkin’s transformation
65C05
Hölder continuity
Yamada–Watanabe approximation
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ISSN0894-9840
1572-9230
DOI10.1007/s10959-021-01082-9

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Summary:The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler–Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for McKean–Vlasov SDEs, where (1) the diffusion terms are Hölder continuous by taking advantage of Yamada–Watanabe’s approximation approach and (2) the drifts are Hölder continuous by freezing distributions followed by invoking Zvonkin’s transformation trick.
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ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-021-01082-9