  In an earlier work made by the first author with J. Turi (Degenerate
Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic
Oscillators, AMO, 2008), the solution of a stochastic variational inequality
modeling an elasto-perfectly-plastic oscillator has been studied. The existence
and uniqueness of an invariant measure have been proven. Nonlocal problems have
been introduced in this context. In this work, we present a new
characterization of the invariant measure. The key finding is the connection
between nonlocal PDEs and local PDEs which can be interpreted with short cycles
of the Markov process solution of the stochastic variational inequality.
