An analytic approach to the ergodic theory of a stochastic variational inequality (Q424744)

From the author's abstract: In an earlier work by the first author and \textit{J. Turi} [Appl. Math. Optim. 58, No. 1, 1--27 (2008; Zbl 1168.60029)], the solution of a stochastic variational inequality modeling an elasto-perfectly-plastic oscillator was studied. Existence and uniqueness of an invariant measure were proven. Nonlocal problems were introduced in this context. In this work, we present a new characterization of the invariant measure. The main result is a connection between nonlocal PDEs and local PDEs which can be interpreted with short cycles of the Markov process solution of the stochastic variational inequality.