A Necessary and Sufficient Condition for Invertibility of Adapted Perturbations of Identity on Wiener Space
نویسنده
چکیده
Let (W,H,μ) be the classical Wiener space, assume that U = IW + u is an adapted perturbation of identity satisfying the Girsanov identity. Then, U is invertible if and only if the kinetic energy of u is equal to the relative entropy of the measure induced with the action of U on the Wiener measure μ, in other words U is invertible if and only if 1 2 ∫
منابع مشابه
Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space
Abstract: Let (W,H,μ) be the classical Wiener space. Assume that U = IW + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration ofW . We give some sufficient analytic conditions on u which imply the invertibility of the map U . In particular it is shown that if u ∈ IDp,1(H) is adapted and if exp( 2‖∇u‖2 − δu) ∈ Lq(μ), where p−1 + q−1 = 1, then IW + u i...
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