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<p>In this paper, we study a broad class of McKean–Vlasov stochastic variational inequalities (MVSVIs), where both the drift coefficient <i>b</i> and the diffusion coefficient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> depend on time <i>t</i>, the state <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> and its distribution <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mu _t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation>. We establish the strong well-posedness, when <i>b</i> grows superlinearly and is locally Lipschitz continuous, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> is locally Hölder continuous, both with respect to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(X_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mu _t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation>. Additionally, we present the first propagation of chaos result for MVSVIs under the same conditions.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Ning Ning,
  • Jing Wu

摘要

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.