1. CJM 2005 (vol 57 pp. 204)
|On the Duality between Coalescing Brownian Motions |
A duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.
Keywords:coalescing Brownian motions, duality, martingale problem,, measure-valued processes
2. CJM 1999 (vol 51 pp. 372)
|Uniqueness for a Competing Species Model |
We show that a martingale problem associated with a competing species model has a unique solution. The proof of uniqueness of the solution for the martingale problem is based on duality technique. It requires the construction of dual probability measures.
Keywords:stochastic partial differential equation, Martingale problem, duality