演講者：李育嘉教授

單　位：國立高雄大學應用數學系

日　期：2010年3月17日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Integration by Parts Formula for Abstract Wiener Measure, Revisited 

摘　要：

The integration by parts formula on infinite dimensional space was initiated by Cameron in 1951, there an integration by parts formula was proved for the classical Wiener measure on the classical Wiener space. Later, in 1964, Donsker also proved the formula and applied it to study Fréchet-Volterra differential equation. After Cameron and Donsker, Kuo generalized the formula to abstract Wiener space for abstract Wiener measure using the calculus developed by Gross and applied it to study Fourier-Wiener transform and to evaluate some functional integral. In this talk we revisit the integration by parts formula formulated on abstract Wiener space by Kuo. We show that the conditions in Kuo's result can be relaxed and the proof can also be simplified. For application, first we characterize the abstract Wiener measure and extend the Stein's lemma to infinite dimensions. Secondly we apply the formula to evaluate some functional integrals.