Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]
Lyons, TJ
Lyons
TJ
Röckner, Michael
Röckner
Michael
Zhang, TS
Zhang
TS
We prove that for a given symmetric Dirichlet form of type E(u,upsilon) = integral(E)[A(z)del u(z), del upsilon(z)](H) mu(dz) with E = C-0[0, 1] and H = classical Cameron-Martin space the corresponding diffusion process (under P-mu) 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.
64
1
31-38
31-38
Elsevier
1996