# zbMATH — the first resource for mathematics

Anticipative diffusion and related change of measures. (English) Zbl 0804.60072
The authors consider anticipating drifts of the form $$G(t)= \int_ 0^ t g(s,w) ds$$, $$t\in [0,1]$$, in the standard Wiener space $$\Omega$$. If $$g$$ is square integrable, under some assumptions on its Lipschitz norm one can find $$e_ g$$ such that for all bounded measurable $$\varphi$$ on $$\Omega$$, $$E[\varphi (\cdot+ G)e_ g]= E\varphi$$. This formula for $$e_ g$$ enables to obtain estimates on its moments. The approach is based on the embedding of the shift by $$G$$ in a suitable flow which evolves from the identity transformation.

##### MSC:
 60J65 Brownian motion
Full Text: