ON REFLECTING DIFFUSION-PROCESSES AND SKOROKHOD DECOMPOSITIONS

Let G be a d-dimensional bounded Euclidean domain, H-1(G) the set of f in L2(G) such that delf (defined in the distribution sense) is in L2(G). Reflecting diffusion processes associated with the Dirichlet spaces (H-1(G), E) on L2(G, rhodx) are considered in this paper, where [GRAPHICS] A = (a(ij)) is a symmetric, bounded, uniformly elliptic d x d matrix-valued function such that a(ij) is-an-element-of H-1(G) for each i, j, and rho is-an-element-of H-1(G) is a positive bounded function on G which is bounded away from zero. A Skorokhod decomposition is derived for the continuous reflecting Markov processes associated with (H-1(G), E) having starting points in G under a mild condition which is satisfied when partial derivative G has finite (d - 1)-dimensional lower Minkowski content.