Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations

The paper deals with the infinite-dimensional stochastic equation dX= B(t, X) dt + dW driven by a Wiener process which may also cover stochastic partial differential equations. We study a certain finite dimensional approximation of B(t, X) and give a qualitative bound for its rate of convergence to be high enough to ensure the weak uniqueness for solutions of our equation. Examples are given demonstrating the force of the new condition. Received: 6 November 1999 / Revised version: 21 August 2000 / Published online: 6 April 2001