- Date : 13 Mar. (Thu)
- Place: W.W. 7th-floor, 4th lab.
- Time : 16:30 – 18:00
- Speaker: Dai Taguchi (Ritsumeikan University)
- Title: Gaussian estimate of density of SDE with irregular coefficients and its application to the stability ploblems
- Abstract: We consider the density of a one-dimensional SDEs with bounded measurable drift coefficient and Hölder continuous diffusion coefficient. It is known that if coefficients are smooth enough, the density of SDE is bounded above and below by Gaussian densities. In this talk, we will prove that if the drift coefficient is bounded measurable and diffusion coefficient is bounded, uniformly elliptic and Hölder continuous, then the density of SDE can be bounded above by Gaussian density. The idea of proof is a “Taylor-like expansion” of semigroup and density which is introduced by Bally and Kohatsu-Higa.
As an application of the density estimate, we provide the strong rate of convergence for the stability problems with discontinuous drift coefficient and Hölder continuous diffusion coefficient.
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