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A stochastic variational inequality is proposed to model an elasto-plasticoscillator excited by a filtered white noise. We prove the ergodic propertiesof the process and characterize the corresponding invariant measure. Thisextends Bensoussan-Turi's method (Degenerate Dirichlet Problems Related to theInvariant Measure of Elasto-Plastic Oscillators, AMO, 2008) with a significantadditional difficulty of increasing the dimension. Two points boundary valueproblem in dimension 1 is replaced by elliptic equations in dimension 2. In thepresent context, Khasminskii's method (Stochastic Stability of DifferentialEquations, Sijthoff and Noordhof,1980) leads to the study of degenerateDirichlet problems with partial differential equations and nonlocal boundaryconditions.

Degenerate Dirichlet Problems Related to the Ergodic Property of an Elasto-Plastic Oscillator Excited by a Filtered White Noise