Communications on Pure and Applied Analysis (CPAA)

Action minimizing stochastic invariant measures for a class of Lagrangian systems

Pages: 1211 - 1223, Volume 7, Issue 5, September 2008      doi:10.3934/cpaa.2008.7.1211

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Kaizhi Wang - College of Mathematics, Jilin University, Changchun 130012, China (email)

Abstract: In this paper we discuss a variational method of constructing an action minimizing stochastic invariant measure for positive definite Lagrangian systems. Then we study some main properties of the stochastic minimal measures. Finally we give the definitions of stochastic Mather's functions with respect to the stochastic differential equation d$x=v(t)$d$t+\sigma(x)$d$w$ and prove their differentiability.

Keywords:  Action minimizing stochastic invariant measures, Lagrangian systems, stochastic Mather's functions, variational method.
Mathematics Subject Classification:  Primary: 37H99; Secondary: 37J50.

Received: October 2007;      Revised: April 2008;      Available Online: June 2008.