Brownian Motion on a Pseudo Sphere in Minkowski Space R^l_v
Abstract
For a Brownian motion moving on a pseudo sphere in Minkowski space R^l_v of radius r starting from point X, we obtain the distribution of hitting a fixed point on this pseudo sphere with l≥ 3 by solving Dirichlet problems. The proof is based on the method of separation of variables and the orthogonality of trigonometric functions and Gegenbauer polynomials.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- October 2016
- DOI:
- 10.1007/s10955-016-1574-0
- Bibcode:
- 2016JSP...165..164J
- Keywords:
-
- Brownian motion;
- Minkowski space;
- Dirichlet problem;
- Laplacian-Beltrami operator;
- Hypergeometric functions;
- Gegenbauer polynomials