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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
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