Rate of homogenization for fully-coupled McKean–Vlasov SDEs
Zachary Bezemek, Leonidas Spiliopoulos
Abstract
In this paper, we consider a fully-coupled slow–fast system of McKean–Vlasov stochastic differential equations with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy problem on the Wasserstein space that are of independent interest.
Topics & Concepts
MathematicsHomogenization (climate)ErgodicityErgodic theoryStochastic differential equationApplied mathematicsInitial value problemCauchy distributionMathematical analysisRate of convergenceStatisticsEngineeringChannel (broadcasting)EcologyBiodiversityElectrical engineeringBiologyAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applicationsNonlinear Partial Differential Equations