From Reflecting Brownian Motion to Reflected Stochastic Differential Equations: A Systematic Survey and Complementary Study

20 Pages Posted: 27 Oct 2020

See all articles by Yunwen Wang

Yunwen Wang

Department of Statistics, University of Warwick

Jinfeng LI

Department of Electrical and Electronic Engineering, Imperial College London

Date Written: September 7, 2020

Abstract

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem’s solution to more general cases is investigated, based on which a discussion is further conducted on the existence of solutions for a few particular kinds of stochastic differential equations with a reflected boundary. It is proved that the multidimensional version of the Skorohod equation can be solved under the assumption of a convex domain (D).

Keywords: stochastic process, reflecting Brownian motion, Skorohod problem, stochastic differential equation

Suggested Citation

Wang, Yunwen and LI, Jinfeng, From Reflecting Brownian Motion to Reflected Stochastic Differential Equations: A Systematic Survey and Complementary Study (September 7, 2020). Available at SSRN: https://ssrn.com/abstract=3688563 or http://dx.doi.org/10.2139/ssrn.3688563

Yunwen Wang

Department of Statistics, University of Warwick ( email )

Department of Statistics,
University of Warwick
Coventry, West Midlands CV4 7AL
United Kingdom

Jinfeng LI (Contact Author)

Department of Electrical and Electronic Engineering, Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/jinfeng.li

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
45
Abstract Views
278
PlumX Metrics