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Semiclassical analysis and a new result for Poisson-Lévy excursion measures

Ian Davies Orcid Logo

Electronic Journal of Probability, Volume: 13, Issue: 45, Pages: 1283 - 1306

Swansea University Author: Ian Davies Orcid Logo

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Abstract

The Poisson-Lévy excursion measure for the diffusion process with small noisesatisfying the Itô equationdX^{\varepsilon} = b(X^{\varepsilon}(t))dt + \sqrt\varepsilon\,dB(t)is studied and the asymptotic behaviour in $\varepsilon$ is investigated. The leadingorder term is obtained exactly and it is sh...

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Published in: Electronic Journal of Probability
ISSN: 1083-6489
Published: 2008
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URI: https://cronfa.swan.ac.uk/Record/cronfa1056
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first_indexed 2013-07-23T11:46:12Z
last_indexed 2018-02-09T04:27:55Z
id cronfa1056
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spelling 2014-01-28T13:52:59.2264666 v2 1056 2011-10-01 Semiclassical analysis and a new result for Poisson-Lévy excursion measures 3eddb437f814b8134d644309f8b5693c 0000-0002-4872-5786 Ian Davies Ian Davies true false 2011-10-01 SMA The Poisson-Lévy excursion measure for the diffusion process with small noisesatisfying the Itô equationdX^{\varepsilon} = b(X^{\varepsilon}(t))dt + \sqrt\varepsilon\,dB(t)is studied and the asymptotic behaviour in $\varepsilon$ is investigated. The leadingorder term is obtained exactly and it is shown that at an equilibrium point there areonly two possible forms for this term - Lévy or Hawkes -- Truman. We also compute the next to leading order term and demonstrate the remarkable fact that it is identically zero. Journal Article Electronic Journal of Probability 13 45 1283 1306 1083-6489 14 8 2008 2008-08-14 http://ejp.ejpecp.org/article/view/513 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2014-01-28T13:52:59.2264666 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Ian Davies 0000-0002-4872-5786 1
title Semiclassical analysis and a new result for Poisson-Lévy excursion measures
spellingShingle Semiclassical analysis and a new result for Poisson-Lévy excursion measures
Ian Davies
title_short Semiclassical analysis and a new result for Poisson-Lévy excursion measures
title_full Semiclassical analysis and a new result for Poisson-Lévy excursion measures
title_fullStr Semiclassical analysis and a new result for Poisson-Lévy excursion measures
title_full_unstemmed Semiclassical analysis and a new result for Poisson-Lévy excursion measures
title_sort Semiclassical analysis and a new result for Poisson-Lévy excursion measures
author_id_str_mv 3eddb437f814b8134d644309f8b5693c
author_id_fullname_str_mv 3eddb437f814b8134d644309f8b5693c_***_Ian Davies
author Ian Davies
author2 Ian Davies
format Journal article
container_title Electronic Journal of Probability
container_volume 13
container_issue 45
container_start_page 1283
publishDate 2008
institution Swansea University
issn 1083-6489
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://ejp.ejpecp.org/article/view/513
document_store_str 0
active_str 0
description The Poisson-Lévy excursion measure for the diffusion process with small noisesatisfying the Itô equationdX^{\varepsilon} = b(X^{\varepsilon}(t))dt + \sqrt\varepsilon\,dB(t)is studied and the asymptotic behaviour in $\varepsilon$ is investigated. The leadingorder term is obtained exactly and it is shown that at an equilibrium point there areonly two possible forms for this term - Lévy or Hawkes -- Truman. We also compute the next to leading order term and demonstrate the remarkable fact that it is identically zero.
published_date 2008-08-14T03:02:42Z
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score 11.035634

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