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Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise


 
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1. Title Title of document Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise
 
2. Creator Author's name, affiliation, country Arnaud Debussche; ENS Cachan Bretagne
 
2. Creator Author's name, affiliation, country Michael Hoegele; Universität Potsdam
 
2. Creator Author's name, affiliation, country Peter Imkeller; Humboldt-Universität zu Berlin
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stochastic reaction diffusion equation with heavy-tailed L'evy noise; first exit times; regularly varying L'evy process; small noise asymptotics;
 
3. Subject Subject classification 60H15; 60G51; 35R69; 60J75; 92F99
 
4. Description Abstract This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump L'evy noise in the limit of small noise intensity. It is shown that the law of the suitably renormalized first exit times from the domain of attraction of a stable state converges to an exponential law of parameter 1 in a strong sense of Laplace transforms, including exponential moments. As a consequence, the expected exit times increase polynomially in the inverse intensity, in contrast to Gaussian perturbations, where this growth is known to be of exponential rate.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) IRTG SMCP Berlin-Zurich; Berlin Mathematical School
 
7. Date (YYYY-MM-DD) 2011-04-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1622
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1622
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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