A Measure-on-Graph-Valued Diffusion: A Particle System with Collisions and Its Applications

A diffusion-taking value in probability-measures on a graph with vertex set V, ∑i∈Vxiδi is studied. The masses each satisfy the stochastic differential equation of form dxi=∑j∈N(i)xixjdBij simplex, where {Bij} are independent standard Brownian motions skew symmetry, and N(i) neighbour i. dual Markov chain integer partitions to semigroup associated diffusion used show that support an extremal stationary state adjoint graph. We also investigate linear drift, which gives killing finite lattice. study unique diffusion, generalizes Dirichlet distribution. Two applications diffusions discussed: analysis algorithm find graph, Bayesian selection based computation probability sample by using coupling from past.