Well-Posedness and Propagation of Chaos for McKean–Vlasov Stochastic Variational Inequalities

Ning Ning and Jing Wu ()
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Ning Ning: Texas A&M University
Jing Wu: Sun Yat-sen University

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-48

Abstract: Abstract In this paper, we study a broad class of McKean–Vlasov stochastic variational inequalities (MVSVIs), where both the drift coefficient b and the diffusion coefficient $$\sigma $$ σ depend on time t, the state $$X_t$$ X t and its distribution $$\mu _t$$ μ t . We establish the strong well-posedness, when b grows superlinearly and is locally Lipschitz continuous, and $$\sigma $$ σ is locally Hölder continuous, both with respect to $$X_t$$ X t and $$\mu _t$$ μ t . Additionally, we present the first propagation of chaos result for MVSVIs under the same conditions.

Keywords: Stochastic variational inequalities; Locally Hölder continuous; Well-posedness; Propagation of chaos; 60H10; 60J60; 60K35 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01459-0

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