  A stochastic variational inequality is proposed to model an elasto-plastic
oscillator excited by a filtered white noise. We prove the ergodic properties
of the process and characterize the corresponding invariant measure. This
extends Bensoussan-Turi's method (Degenerate Dirichlet Problems Related to the
Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008) with a significant
additional difficulty of increasing the dimension. Two points boundary value
problem in dimension 1 is replaced by elliptic equations in dimension 2. In the
present context, Khasminskii's method (Stochastic Stability of Differential
Equations, Sijthoff and Noordhof,1980) leads to the study of degenerate
Dirichlet problems with partial differential equations and nonlocal boundary
conditions.
