Speaker : Professor Arturo Kohatsu-Higa (Ritsumeikan University, Japan)
Title : On the smoothness of the fundamental solution for some non-elliptic partial differential equation with non-smooth coefficients
Time : 2011-12-19 (Mon) 15:00 - 16:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: We consider in a stochastic framework an equation of the type : The above equation appears in a variety of application fields such as filltering and finance when considering models with regime change. From the mathematical point of view, the above system is inherently non-elliptic. We suppose that b is measurable and bounded, and are smooth and the system is uniformly hypo-elliptic with uniformly elliptic.In this setting, we prove that the density of Y is smooth on the whole space. We also give a general integration by parts formula in in infinite dimensional space which helps to obtain other properties of the density of Y.