Comparisons for measure valued processes with interactions

• 成果类型: Article
• 署名作者: Jacka, S; Tribe, R
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 1679-1712
• 关键词: Diffusions

摘要

This paper considers some measure-valued processes {X-t:t is an element of [0, T]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Phi of the process are given that imply that the expectations E(Phi(X-T)) are comparable to the constant branching case. Applications to hitting estimates and regularity of solutions are discussed. The result is established via the martingale optimality principle of stochastic control theory. Key steps, which are of independent interest, are the proof of a version of Ito's lemma for Phi(X-t), suitable for a large class of functions of measures (Theorem 3) and the proof of various smoothing properties of the Dawson-Watanabe transition semigroup (Section 3).