Some asymptotic formulars for a Brownian motion whose dimension is variable with a regular variation from a parabolic domain to research the variation of biological species
Year: 2020
Type: preprint
Abstract: Consider a Brownian motion with a regular variation starting at an interior point of a domain D in R d+1 ,d ≥ 1, let τ D denote the first time the Brownian motion exits from D. Estimates with exact constants for the asymptotics of logP(τ D > T) are given for T → ∞, depending on the shape of the domain D and the order of the regular variation. Furthermore, the asymptotically equivalence are obtained. The problem is motivated by the early results of Lifshits and Shi, Li in the first exit time and Karamata in the regular variation. The methods of proof are based on their results and the calculus of variations.
Authors: Xiaoming Li, Wenbin Che, Jingjun Zhang
Institution: Qihoo 360 (China)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4235867494