This is a preprint, a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Research
Upper and lower bounds of the first exit time of Brownian motion from The Minimum and Maximun Parabolic Domains with variable dimension to research the variation of biological species
Jingjun Zhang
Qihoo 360 Technology Company, Beijing, China
Corresponding Author
ORCiD: https://orcid.org/0000-0002-7025-3789
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Consider a Brownian motion with variable dimension starting at an interior point of the minimum or maximum parabolic domains Dmax t and Dmin t in Rd(t)+2, d(t) ≥ 1 is an increasing integral function as t →∞,d(t) →∞, and let τDmax t and τDmin t denote the first time the Brownian motion exits from Dmax t and Dmin t , respectively. Upper and lower bounds with exact constants for the asymptotics of logP(τDmax t > t) and logP(τDmin t > t) are given as t → ∞, depending on the shape of the domain Dmax t and Dmin t . The methods of proof are based on Gordon’s inequality and early works of Li, Lifshits and Shi in the single general parabolic domain case.
Keywords
Brownian motion, Variable dimension, Gordon’s inequality
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 23 Jun, 2020
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mathematical and Theoretical Biology
Learn more about our company.
This is a preprint. It has not completed peer review.
Research
Upper and lower bounds of the first exit time of Brownian motion from The Minimum and Maximun Parabolic Domains with variable dimension to research the variation of biological species
Jingjun Zhang
Qihoo 360 Technology Company, Beijing, China
Corresponding Author
ORCiD: https://orcid.org/0000-0002-7025-3789
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 23 Jun, 2020
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mathematical and Theoretical Biology
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Consider a Brownian motion with variable dimension starting at an interior point of the minimum or maximum parabolic domains Dmax t and Dmin t in Rd(t)+2, d(t) ≥ 1 is an increasing integral function as t →∞,d(t) →∞, and let τDmax t and τDmin t denote the first time the Brownian motion exits from Dmax t and Dmin t , respectively. Upper and lower bounds with exact constants for the asymptotics of logP(τDmax t > t) and logP(τDmin t > t) are given as t → ∞, depending on the shape of the domain Dmax t and Dmin t . The methods of proof are based on Gordon’s inequality and early works of Li, Lifshits and Shi in the single general parabolic domain case.
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.