STA 290 Seminar Series
Thursday, October 1st, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Tomoyuki Ichiba (UC Santa Barbara)
Title: “Walsh semimartingales and diffusions on metric graphs”
Abstract: In this talk we shall discuss diffusions 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 examine its solution. The stationary distribution, strong Markov property and related statistical problems are also discussed. Then we extend our considerations to diffusions on metric graphs. This talk is based on joint work with I. Karatzas, V. Prokaj and M. Yan.