STOCHASTIC EQUATION AND EXPONENTIAL ERGODICITY IN WASSERSTEIN DISTANCES FOR AFFINE PROCESSES

• 成果类型: Article
• 署名作者: Friesen, Martin; Jin, Peng; Rudiger, Barbara
• 署名单位: University of Wuppertal; Shantou University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1554
• 发表日期: 2020
• 页码: 2165-2195
• 关键词: state branching-processes; multitype continuous-state; continuous-time; asymptotic properties; limit distributions; diffusion-processes; immigration; moments; GROWTH

摘要

This work is devoted to the study of conservative affine processes on the canonical state space D = R-+(m) x R-n, where m + n > 0. We show that each affine process can be obtained as the pathwise unique strong solution to a stochastic equation driven by Brownian motions and Poisson random measures. Then we study the long-time behavior of affine processes, that is, we show that under first moment condition on the state-dependent and log-moment conditions on the state-independent jump measures, respectively, each subcritical affine process is exponentially ergodic in a suitably chosen Wasserstein distance. Moments of affine processes are studied as well.