# Meeting Details

Title: On stochastic completeness of a jump process and its application to graphs Seminar on Probability and its Application Jun Masamune, Penn State University Altoona In 1986, A Grigoryan discovered a sharp volume-growth condition for the Brownian motion on a Riemannian manifold to be stochastically complete; namely, non-explosive. This condition was extended to a diffusion process on a metric measure space by K.Th. Sturm in 1994. Quite recently, R.K. Wojciechowski constructed a stochastically incomplete graph that satisfies this condition with respect to the graph distance. In this talk, I will introduce a new volume-growth condition for a jump-process on a metric measure space that is stochastically complete, then I will apply that result to a graph. Wojciechowski's example confirms that our condition for a graph is sharp. This result was obtained in a collaboration with Alexander Grigoryan and Xeuping Huang (Bielefeld, Germany).

### Room Reservation Information

Room Number: MB106 02 / 25 / 2011 02:20pm - 03:20pm