INVARIANCE PRINCIPLE FOR VARIABLE SPEED RANDOM WALKS ON TREES

• 成果类型: Article
• 署名作者: Athreya, Siva; Loehr, Wolfgang; Winter, Anita
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Bangalore; University of Duisburg Essen
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1071
• 发表日期: 2017
• 页码: 625-667
• 关键词: brownian-motion; CONVERGENCE; LIMITS

摘要

We consider stochastic processes on complete, locally compact tree-like metric spaces (T,r) on their natural scale with boundedly finite speed measure ?. Given a triple (T,r,nu) such a speed-nu motion on (T,r) can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all x,y is an element of T and all positive, bounded measurable f, E-x[integral(tau y)(0)dsf(X-s)]=2 integral(T)nu(dz)r(y,c(x,y,z))f(z)