Jacka, Saul D. and Hernández-Hernández, Ma Elena (2021) Minimising the expected commute time. Stochastic Processes and their Applications . doi:10.1016/j.spa.2019.04.010 ISSN 0304-4149.

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Abstract

Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to $1$ and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion's drift via the corresponding scale function. In the static version the diffusion's drift can be chosen at each point in [0,1], whereas in the dynamic version we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title:	Stochastic Processes and their Applications
Publisher:	Elsevier Science BV
ISSN:	0304-4149
Official Date:	2021
Dates:	Date Event 2021 Published 16 May 2019 Available 23 April 2019 Accepted
DOI:	10.1016/j.spa.2019.04.010
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	24 April 2019
Date of first compliant Open Access:	16 May 2020
Funder:	EPSRC
Grant number:	EP/P00377X/1 and EP/N510129/1

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