Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 11--22

ON THE INTEGRAL OF THE SUM OF SQUARED ORNSTEIN-UHLENBECK PROCESSES

By

MARIO LEFEBVRE, École Polytechnique de Montréal

SUMMARY. Let dx(t)/dt = y2(t)+z2(t), where y(t) and z(t) are independent Ornstein-Uhlenbeck processes, and let T(y,z) be the first time the two-dimensional diffusion process (y(t),z(t)), starting from (y,z), hits either of two concentric circles. The moment generating function and the mean of x[T(y,z)] are computed explicitly. The cases when there is a single boundary are also treated.

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

Key words and phrases. First passage, integrated process, multidimensional processes.

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