摘要:
A picture of abstract Wiener space is the R infinite random variable with component being iid standard normal. The classical Wiener space is a particular case. The L2 space has simple structure by Wiener chaos decomposition. In classical Wiener space, the functions in level n is the n- multiple Wiener integrals. This is the basic for the Malliavin calculus. We use this to construct more “regular” (smooth) functions that the nth order derivative can be defined. The Sobolev space will be defined as in finite dimensional Euclidean space.We plan to meet on every Friday for several weeks to learn the basic idea from the following book.
姜祖恕、須上苑、許順吉will share for the reading and the presentation.
參考：Ichiro Shigekawa, Stochastic Analysis,
AMS TranslationMath Monograph 224
A picture of abstract Wiener space is the R infinite random variable with component being iid standard normal. The classical Wiener space is a particular case. The L2 space has simple structure by Wiener chaos decomposition. In classical Wiener space, the functions in level n is the n- multiple Wiener integrals. This is the basic for the Malliavin calculus. We use this to construct more “regular” (smooth) functions that the nth order derivative can be defined. The Sobolev space will be defined as in finite dimensional Euclidean space.We plan to meet on every Friday for several weeks to learn the basic idea from the following book.
姜祖恕、須上苑、許順吉will share for the reading and the presentation.
參考：Ichiro Shigekawa, Stochastic Analysis,
AMS TranslationMath Monograph 224