演講訊息 TALKS

This is a study seminar on Malliavin calculus. The theory of Malliavin calculus is a differential calculus on the Wiener space. This is the probability space where the Brownian motion ( and other diffusion processes) lives. It is known that there is a close connection of a diffusion process and a second order parabolic equation. The transition probability distribution of this diffusion process satisfies a second order parabolic equation. As a consequence, the transition density is the fundamental solution of a parabolic equation which exists as a result of the theory of partial differential equation. Malliavin calculus, invented by Malliavin in 1970’s, is a probabilistic approach to prove this result. He went further to use his new idea to prove that Hormander condition implies the existence of a density for the diffusion process. Hormander original proof was based on the theory of partial differential equation. Since the invention of the theory, it has found many applications not only to partial differential equations., but also to stochastic partial differential equations,mathematical finance, to name a few. We plan to meet on every Friday for several weeks to learn the basic idea in the following book. 姜祖恕、須上苑、許順吉will share the presentation.