Martingale decomposition of Dirichlet processes on the Banach space C0[0, 1]

AbstractWe prove that for a given symmetric Dirichlet form of type g(u, v) = ∫E〈A(z)∇u(z), ∇v(z)〉hμ(dz) with E = C0[0, 1] and H = classical Cameron-Martin space the corresponding diffusion process (under Pμ) can be decomposed into a forward and a backward E-valued martingale. The construction of the martingale is direct and explicit since it is based on a modification of Levy's construction of Brownian motion. Applications to prove tightness of laws of diffusions of the above kind are given