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 = y*^{2}(*t*)+*z*^{2}(*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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