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On the one-sided exit problem for stable processes in random scenery


 
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1. Title Title of document On the one-sided exit problem for stable processes in random scenery
 
2. Creator Author's name, affiliation, country Fabienne Castell; Aix-Marseille Université; France
 
2. Creator Author's name, affiliation, country Nadine Guillotin-Plantard; Université de Lyon; France
 
2. Creator Author's name, affiliation, country Françoise Pène; Université de Brest; France
 
2. Creator Author's name, affiliation, country Bruno Schapira; Aix-Marseille Université; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stable process, Random scenery, First passage time, One-sided barrier problem, One-sided exit problem, Survival exponent.
 
3. Subject Subject classification 60F05; 60F17; 60G15; 60G18; 60K37
 
4. Description Abstract

We consider the one-sided exit problem for stable Lévy process in random scenery, that is the asymptotic behaviour for $T$ large of the probability $$\mathbb{P}\Big[ \sup_{t\in[0,T]} \Delta_t \leq 1\Big] $$ where $$\Delta_t = \int_{\mathbb{R}} L_t(x) \, dW(x).$$ Here $W=(W(x))_{x\in\mathbb{R}}$ is a two-sided standard real Brownian motion and $(L_t(x))_{x\in\mathbb{R},t\geq 0}$ the local time of a stable Lévy process with index $\alpha\in (1,2]$, independent from the process $W$. Our result confirms some physicists prediction by Redner and Majumdar.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) French ANR project MEMEMO2 2010 BLAN 0125
 
7. Date (YYYY-MM-DD) 2013-05-14
 
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/2444
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2444
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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