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论文类型：期刊论文

发表时间：2013-09-01

发表刊物：INTERNATIONAL JOURNAL OF BIOMATHEMATICS

收录刊物：SCIE、Scopus

卷号：6

期号：5

ISSN号：1793-5245

关键字：Small ball estimate; biological population; Brownian motion

摘要：Using the theory of small ball estimate to study the biological population for keeping ecological balance in an ecosystem, we consider a Brownian motion with variable dimension starting at an interior point of a general parabolic domain D-t in Rd(t)+1 where d(t) >= 1 is an increasing integral function as t -> infinity, d(t) -> infinity. Let tau D-t denote the first time the Brownian motion exits from D-t. Upper and lower bounds with exact constants of log P(tau D-t > t) are given as t -> infinity, depending on the shape of the domain D-t. The problem is motivated by the early results of Lifshits and Shi, Li, Lu in the exit probabilities. The methods of proof are based on the calculus of variations and early works of Lifshits and Shi, Li, Shao in the exit probabilities of Brownian motion.