Decomposition of a class of functionals

LetX(t) be a symmetric conservative Hunt process. In this paper, we decompose the functionalu(X(t), t) into a sum of a square integrable martingale and a regular 0-quadratic variation process. This paper is based on the author's dissertation, presented for the degree of Doctor of philosophy in Institute of Applied Mathematics, Academia Sinica under the supervision of Prof. Yan Jia-an.