Stochastic integrals in abstract wiener space
Let W(t, ω) be the Wiener process on an abstract Wiener space (i, H, B) corresponding to the canonical normal distributions on H. Stochastic integrals (formula presented) and (formula presented) are defined for non-anticipating transformations f with values in B(B, B) such that (x(t, ω) — I)(B) B* and C with values in H. Suppose (formula presented), where u is a non-anticipating transformation with values in H. Let fit, x be a continuous function on R x B, continuously twice differentiable in the indirections with D2 f(t, x) e H) for the x variable and once differentiable for the t variable. Then (formula presented) where <, > is the inner product of H. Under certain assumptions on A and a it is shown that the stochastic integral equation (formula presented) has a unique solution. This solution is a homogeneous strong Markov process. © 1972 Pacific Journal of Mathematics.
Publication Source (Journal or Book title)
Pacific Journal of Mathematics
Kuo, H. (1972). Stochastic integrals in abstract wiener space. Pacific Journal of Mathematics, 41 (2), 469-483. https://doi.org/10.2140/pjm.1972.41.469