Date: Thursday, April 04, 2013
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: Pathwise Stochastic Taylor Expansion and Forward Path-Dependent PDEs
Abstract: In this talk we first revisit the notion of pathwise stochastic Taylor ex- pansion, and prove a new result that extends our previous works to a more general setting, in terms of the newly developed notion of path-derivative initiated by Dupire. We will then show how this new form of pathwise Tay- lor expansion could lead to a notion of stochastic viscosity solution for a class of fully nonlinear SPDEs and the corresponding Path-dependent PDEs (PPDEs), without having to invoke the stochastic characteristics for the lo- calization. We will discuss the issues of consistency, stability, and comparison principles for the stochastic viscosity solutions. In the semilinear case, we show that the PPDE, whence the SPDE, is well-posed in our new framework.
This is a joint work with Rainer Buckdahn and Jianfeng Zhang.
1528_Michigan-2013.pdf
Speaker: Jin Ma
Institution: USC
Event Organizer: Erhan Bayraktar erhan@umich.edu
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