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Continuity and strict positivity of the multi-layer extension of the stochastic heat equation
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Hang Lun, Chin and Warren, Jon (2020) Continuity and strict positivity of the multi-layer extension of the stochastic heat equation. Electronic Journal of Probability, 25 . 109. doi:10.1214/20-EJP511 ISSN 1083-6489.
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Official URL: https://doi.org/10.1214/20-EJP511
Abstract
We prove the continuity and strict positivity of the multi-layer extension to the stochastic heat equation introduced in [43] which form a hierarchy of partition functions for the continuum directed random polymer. This shows that the corresponding free energy (logarithm of the partition function) is well defined. This is also a step towards proving the conjecture stated at the end of the above paper that an array of such partition functions has the Markov property.
Item Type: | Journal Article | ||||||||
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Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Probability, Mathematical statistics | ||||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||||
ISSN: | 1083-6489 | ||||||||
Official Date: | 2020 | ||||||||
Dates: |
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Volume: | 25 | ||||||||
Article Number: | 109 | ||||||||
DOI: | 10.1214/20-EJP511 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 22 September 2020 | ||||||||
Date of first compliant Open Access: | 23 September 2020 | ||||||||
RIOXX Funder/Project Grant: |
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