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Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion


 
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1. Title Title of document Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion
 
2. Creator Author's name, affiliation, country Romain Abraham; Université René Descartes (Paris 5)
 
2. Creator Author's name, affiliation, country Wendelin Werner; Université Paris-Sud and IUF
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian snakes, superprocesses, non-linear differential equations
 
3. Subject Subject classification 60J25, 60J45
 
4. Description Abstract We investigate the asymptotic behaviour of the probability that a normalized $d$-dimensional Brownian snake (for instance when the life-time process is an excursion of height 1) avoids 0 when starting at distance $\varepsilon$ from the origin. In particular we show that when $\varepsilon$ tends to 0, this probability respectively behaves (up to multiplicative constants) like $\varepsilon^4$, $\varepsilon^{2\sqrt{2}}$ and $\varepsilon^{(\sqrt {17}-1)/2}$, when $d=1$, $d=2$ and $d=3$. Analogous results are derived for super-Brownian motion started from $\delta_x$ (conditioned to survive until some time) when the modulus of $x$ tends to 0.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1997-05-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/17
 
10. Identifier Digital Object Identifier 10.1214/EJP.v2-17
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 2
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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