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hal-00653122, version 1

An analytic approach to the ergodic theory of stochastic variational inequalities

Alain Bensoussan 1, Laurent Mertz () 2

(2011-09-01)

Abstract: 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.

  • 1:  International Center for Decision and Risk Analysis (ICDRiA)
  • University of Texas at Dallas
  • 2:  Laboratoire Jacques-Louis Lions (LJLL)
  • CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
  • Domain : Mathematics/Analysis of PDEs
    Mathematics/Probability
    Engineering Sciences/Mechanics/Vibrations
    Physics/Mechanics/Vibrations
  • Keywords : in équations variationnelles stochastiques – équations aux d ériv ées partielles avec des conditions non-locales – vibrations al éatoires – di ffusion ergodique.
 
  • hal-00653122, version 1
  • http://hal.archives-ouvertes.fr/hal-00653122
  • oai:hal.archives-ouvertes.fr:hal-00653122
  • From: Laurent Mertz <>
  • Submitted on: Sunday, 18 December 2011 07:16:17
  • Updated on: Sunday, 18 December 2011 08:48:34