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MEXIT : Maximal un-coupling times for stochastic processes
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Ernst, Philip A., Kendall, W. S., Roberts, Gareth O. and Rosenthal, Jeff S. (2019) MEXIT : Maximal un-coupling times for stochastic processes. Stochastic Processes and their Applications, 129 (2). pp. 355-380. doi:10.1016/j.spa.2018.03.001 ISSN 0304-4149.
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Official URL: https://doi.org/10.1016/j.spa.2018.03.001
Abstract
Classical coupling constructions arrange for copies of the same Markov process started at two dif- ferent initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two di erent Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this \un-coupling" or \maximal agreement" construction as MEXIT, standing for \maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exempli ed by discussion of MEXIT for Brownian motions with two di erent constant drifts.
| Item Type: | Journal Article | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science) | |||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Stochastic processes | |||||||||||||||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | |||||||||||||||||||||
| Publisher: | Elsevier Science BV | |||||||||||||||||||||
| ISSN: | 0304-4149 | |||||||||||||||||||||
| Official Date: | February 2019 | |||||||||||||||||||||
| Dates: |
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| Volume: | 129 | |||||||||||||||||||||
| Number: | 2 | |||||||||||||||||||||
| Page Range: | pp. 355-380 | |||||||||||||||||||||
| DOI: | 10.1016/j.spa.2018.03.001 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||
| Date of first compliant deposit: | 2 March 2018 | |||||||||||||||||||||
| Date of first compliant Open Access: | 10 April 2019 | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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