Quasi-invariant theorem on the Gaussian path space


主讲人:吴波 复旦大学副研究员




主讲人介绍:吴波,复旦大学副研究员,博士生导师。主要从事随机分析的教学和科研工作,尤其是黎曼轨道空间和环空间上的随机分析,流形上的热核估计及其泛函不等式。在 Prob. The. Relat. Fields、 Ann. Probab.、 J. Funct. Anal.、 SIAM J. Math. Anal.、Tran. Amer. Math. Soc.、J. Geom. Anal.、Stoch. Proc. App. 等权威期刊发表论文20多篇。

内容介绍:In this talk, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the case of the fractional Brownian motion. As applications, we will establish the integration by parts formula and Bismut-Elworthy-Li formula on the Gaussian path space, and by which the logarithmic Sobolev inequality will be presented. Moreover, we will also provide some applications in the field of financial mathematics.