A diffusion process in a Brownian environment with drift
A diffusion process in a Brownian environment with drift
Let $W$ be the space of continuous functions $W$ defined in $R$ and vanishing at the origin.Let $P$ be the Wiener measure on $W$ namely, the probability measure on $W$ such that $\{W(t), t\geqq 0, P\}$ and $\{W(-t), t\geqq 0, P\}$ are independent one-dimensional Brownian motions.Let $\Omega=C[0, \infty)$ and denote …