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Indexed by:期刊论文

Date of Publication:2013-09-01

Journal:INTERNATIONAL JOURNAL OF BIOMATHEMATICS

Included Journals:SCIE、Scopus

Volume:6

Issue:5

ISSN No.:1793-5245

Key Words:Small ball estimate; biological population; Brownian motion

Abstract: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.