Minimising the expected commute time
| Autor: | Saul D. Jacka, Ma Elena Hernández-Hernández |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Stochastic control Diffusion (acoustics) Applied Mathematics 010102 general mathematics Control (management) Markov chain Monte Carlo Sense (electronics) Type (model theory) 01 natural sciences 010104 statistics & probability symbols.namesake Reflection (mathematics) Modeling and Simulation symbols Applied mathematics Point (geometry) 0101 mathematics QA Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 150:729-751 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2019.04.010 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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