On reflecting diffusion processes and Skorokhod decompositions

Let G be a d-dimensional bounded Euclidean domain, H¹ (G) the set of f in L²(G) such that ∇f (defined in the distribution sense) is in L²(G). Reflecting diffusion processes associated with the Dirichlet spaces (H¹(G), ℰ) on L²(G, σd x) are considered in this paper, where[Figure not available: see fulltext.] A=(a^ij is a symmetric, bounded, uniformly elliptic d×d matrix-valued function such that a^ij∈H¹(G) for each i,j, and σ∈H¹(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 (H¹(G), ℰ) having starting points in G under a mild condition which is satisfied when π{variant}G has finite (d-1)-dimensional lower Minkowski content.