Journal article 1168 views
Semiclassical analysis and a new result for Poisson-Lévy excursion measures
Ian Davies 
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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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa1056 |
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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 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
45 |
| Start Page: |
1283 |
| End Page: |
1306 |