Probability Methods For The Convergence Of Finite Difference Approximations To Partial Differential Equations

The paper applies some results on weak convergence of probability measures to the problem of convergence of finite difference approximations to a broad class of degenerate elliptic and parabolic partial differential equations. The equations are of type which arise in stochastic control theory and, generally, have only weak solutions. Interest in the problem stems from interest in stochastic control theory, and in numerical methods for the solution of stochastic control problems. The results are of interest in stochastic control theory and in numerical analysis. Some conditions are stated, the problem is discussed along with its probabilistic interpretation. (Author).