<p>This paper is devoted to establishing the strong averaging principle for a class of slow–fast McKean–Vlasov multivalued stochastic evolution equations in the variational framework. We first establish existence and uniqueness of solutions for this type of stochastic evolution equations. Then we study the averaging principle and prove that the slow component converges in strong sense to the solution of the averaged equation. The main results of this paper are applicable to slow–fast McKean–Vlasov stochastic differential equations with normal reflections in convex domains and slow–fast McKean–Vlasov stochastic variational inequalities. In particular, convergence order is obtained for McKean–Vlasov stochastic evolution equations reflected in convex domains.</p>

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Averaging Principle for Slow–Fast McKean–Vlasov Multivalued Stochastic Evolution Equations

  • Yawen Huang,
  • Jing Wu

摘要

This paper is devoted to establishing the strong averaging principle for a class of slow–fast McKean–Vlasov multivalued stochastic evolution equations in the variational framework. We first establish existence and uniqueness of solutions for this type of stochastic evolution equations. Then we study the averaging principle and prove that the slow component converges in strong sense to the solution of the averaged equation. The main results of this paper are applicable to slow–fast McKean–Vlasov stochastic differential equations with normal reflections in convex domains and slow–fast McKean–Vlasov stochastic variational inequalities. In particular, convergence order is obtained for McKean–Vlasov stochastic evolution equations reflected in convex domains.