Atsushi Takeuchi: Positivity of Densities for Stochastic Differential Equations Driven by Gamma Processes

In this talk, we shall consider stochastic differential equations driven by gamma processes, whose coefficients of the jump terms satisfy the invertible condition and the uniformly elliptic condition. It is well known that the probability law of the solution process is absolutely continuous with respect to the Lebesgue measure, via the integration by parts formula based upon the Girsanov transform. Our goals in this talk are to study the sensitivity analysis, and the error estimate on the densities between the solution process and the driving gamma process, which enables us to discuss the lower bounds and the strict positivity on the density of the solution process. The Malliavin calculus by making full use of measure changes with respect to the Girsanov transform on gamma processes, plays crucial roles in our argument. This is based upon the joint work with Vlad Bally (Université Paris-Est Marne-la-Vallée, France)