Naslov
A characterization of Brownian motion on Sierpinski spaces

Autori
Vondraček, Zoran

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Seminar on Stochastic Processes, 1991

Urednik/ci
Cinlar, E. ; Chung, K.L. ; Sharpe, M.J.

Izdavač
Birkhäuser

Grad
Boston : Basel : Berlin

Godina
1992

Raspon stranica
233-243

ISBN
0-8176-3628-5

Ključne riječi
Brownian motion on Sierpinski spaces, time-change. exit distributions. harmonic functions for Brownian motion, multidimensional analogues of the Sierpinski gasket

Sažetak
Let $K$ denote the Sierpinski gasket. The natural boundary of $K$ is formed by vertices $a\sb 1$, $a\sb 2$, $a\sb 3$ of the smallest triangle containing $K$. Let $(X\sb t, P\sp x)$ be a Brownian motion on $K\sp 0=K\backslash\{; ; ; a\sb 1, a\sb 2, a\sb 3\}; ; ; $ killed upon hitting the boundary. Let $(Y\sb t, Q\sp x)$ be any diffusion on $K\sp 0$ having the same exit distributions as $X$: $$P\sp x(X\sb{; ; ; \zeta-}; ; ; =a\sb j)=Q\sp x(Y\sb{; ; ; \tilde\zeta}; ; ; =a\sb j)$$ for $j=1, 2, 3$ and for all $x\in K\sp 0$ (where $\zeta$ and $\tilde\zeta$ are corresponding lifetimes). It is proved that $Y$ is a time-change of $X$, thus showing that harmonic functions for Brownian motion on the gasket completely determine the potential theory. Results are proven for Sierpinski spaces, multidimensional analogues of the Sierpinski gasket.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA