**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 2, pp. 179--185

**ON THE FIRST PASSAGE TIME PROBABILITY PROBLEM FOR BIDIMENSIONAL ORNSTEIN-UHLENBECK**

By

MARIO LEFEBVRE, *Ecole Polytechnique de Montréal*

SUMMARY. Bidimensional diffusion processes, the components of which are independent Ornstein-Uhlenbeck processes with the same infinitesimal parameters, are considered. Explicit solutions are obtained, in terms of the moment generating function, to first passage time problems by using the method of similarity solutions. The boundary is either a straight line or a circle and is absorbing.

*AMS (1991) subject classification.* 60J70, 60J60.

*Key words and phrases.* Absorption time, bidimensional processes, similarity solutions.