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Ergodic Properties of Multidimensional Brownian Motion with Rebirth


 
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1. Title Title of document Ergodic Properties of Multidimensional Brownian Motion with Rebirth
 
2. Creator Author's name, affiliation, country Ilie Grigorescu; University of Miami
 
2. Creator Author's name, affiliation, country Min Kang; North Carolina State University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Dirichlet Laplacian, Green function, analytic semigroup, jump diffusion
 
3. Subject Subject classification 60J35; 60J75; 35K15; 91B24; 92D10
 
4. Description Abstract In a bounded open region of the $d$ dimensional space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. The evolution is invariant with respect to a density equal, modulo a constant, to the Green function of the Dirichlet Laplacian centered at the point of return. We calculate the resolvent in closed form, study its spectral properties and determine explicitly the spectrum in dimension one. Two proofs of the exponential ergodicity are given, one using the inverse Laplace transform and properties of analytic semigroups, and the other based on Doeblin's condition. Both methods admit generalizations to a wide class of processes.
 
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7. Date (YYYY-MM-DD) 2007-10-19
 
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/450
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-450
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
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