A0780
Title: A measure-on-graph-valued diffusion: A particle system with collisions and its application
Authors: Shuhei Mano - The Institute of Statistical Mathematics (Japan) [presenting]
Abstract: A diffusion-taking value in probability measures on a graph is studied. The masses on each vertex satisfy the stochastic differential equation of the form $dx_i = \sum_{j\in N(i)} \sqrt{x_ix_j} dB_{ij}$ on the simplex, where $B_{ij}$ are independent standard Brownian motions with skew symmetry, and N(i) is the neighbor of the vertex i. A dual Markov chain is introduced to the Markov semigroup on integer partitions or an interacting particle system. The diffusion with linear drift that causes the killing of the dual Markov chain is investigated. The Markov chain is used to study the unique stationary state of the diffusion, which generalizes the Dirichlet distribution. An application of the results is illustrated by a Bayesian graph selection problem.
