Journal article 1112 views
Semiclassical analysis and a new result for Poisson-Lévy excursion measures
Electronic Journal of Probability, Volume: 13, Issue: 45, Pages: 1283 - 1306
Swansea University Author:
Ian Davies
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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...
Published in: | Electronic Journal of Probability |
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ISSN: | 1083-6489 |
Published: |
2008
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URI: | https://cronfa.swan.ac.uk/Record/cronfa1056 |
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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 |
|
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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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1763749461723447296 |
score |
11.021648 |