演講訊息 TALKS

摘要： In this seminar series, we plan to study the basic theory of stochastic differential equations. We will mainly follow the lecture note by Prevot-Rochner (2007). The approach is to consider SPDE as a partial differential equation with the noise which is a Wiener process taking values in a Hilbert space or Banach space. This approach leads to the study of martingale theory in infinite dimensional spaces (Hilbert spaces or Banach spaces), and also the stochastic integrals with respect to the Hilbert space valued martingale. We will also have chance to compare different approaches by Walsh (white noise and martingale measure) and also Da Prato-Zabczyk (in Hairer lecture note). Last year, Shang-Yuan Shiu discussed Walsh’s approach. We hope to find chance to come back to this again this year. References: 1. R. C. Dalang, D. Khoshnevisan, C. Mueller, D. Nualart and Y. Xiao (2008), A Mini-course on Stochastic Partial Differential Equation, Lcture Note in Mathematics, 1962 2. C. Prevot and M. Rochner (2007), A Concise Course on Stochastic Partial Differential Equations, Lecture Note in Mathematics, 1905 3. Martin Hairer (2009), An Introduction to Stochastic PDEs 4. J.B. Walsh (1986), An Introduction to Stochastic Partial Differential Equations, Lecture Note in Mathematics, 1108