Friday, March 10 at 3:30pm to 4:30pm
Kaprielian Hall (KAP), 414
3620 South Vermont Avenue, Los Angeles, CA 90089
Tomoyuki Ichiba, UC Santa Barbara
In this talk we shall discuss diffusion on metric graphs. We start with a change-of-variable formula of Freidlin-Sheu type for Walsh semimartingale on a star graph. In diffusion case we characterize such processes via martingale problem. As a consequence of folding/unfolding semimartingale, we obtain a system of degenerate stochastic differential equations and we examine its solution and convergence properties. The stationary distribution, strong Markov property and related statistical problems are also discussed. Then we extend our considerations to diffusion on metric graphs. Part of this talk is based on joint work with I. Karatzas, V. Prokaj, A. Sarantsev and M. Yan.