Action minimizing stochastic invariant measures for a class of Lagrangian systems
Kaizhi Wang · Communications on Pure & Applied Analysis · 2008
In this paper we discuss a variational method of constructing anaction minimizing stochastic invariant measure for positivedefinite Lagrangian systems. Then we study some main properties ofthe stochastic minimal measures. Finally we give the definitionsof stochastic Mather's functions with respect to the stochasticdifferential equationd$x=v(t)$d$t+\sigma(x)$d$w$ and provetheir differentiability.