Fluctuations of Brownian motion with drift

Consider 3 dimensional Brownian motion started on the unit sphere $\{|x|=1\}$ with initial density $\rho$. Let $\rho_t$ be the first hitting density on the sphere $\{|x|=t+1\}$, $t > 0$. Then the linear operators $T_t$ defined by $T_t$ $\rho=\rho_t$ form a semigroup with an infinitesimal generato...

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Veröffentlicht in:Publicacions matemàtiques 1999, Vol.43 (1), p.85-125
Hauptverfasser: Conlon, J. G., Olsen, P.
Format: Artikel
Sprache:eng
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Zusammenfassung:Consider 3 dimensional Brownian motion started on the unit sphere $\{|x|=1\}$ with initial density $\rho$. Let $\rho_t$ be the first hitting density on the sphere $\{|x|=t+1\}$, $t > 0$. Then the linear operators $T_t$ defined by $T_t$ $\rho=\rho_t$ form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift $\bold b$, where $\bold b$ is small in a suitable scale invariant norm.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_43199_04