Speaker :
| Professor Arturo Kohatsu-Higa (Ritsumeikan University, Japan) |
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Title :
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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) |
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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. |
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