BROWNIAN REPRESENTATIONS OF CYLINDRICAL LOCAL MARTINGALES, MARTINGALE PROBLEM AND STRONG MARKOV PROPERTY OF WEAK SOLUTIONS OF SPDES IN BANACH SPACES


    loading  Checking for direct PDF access through Ovid

Abstract

The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property.

    loading  Loading Related Articles