Abstract
We consider the two-dimensional process ( x( t), y( t)), where y( t)=d x( t)/d t is an Ornstein-Uhlenbeck process, Let T be the smallest t for which y( t) = υ. In this note we obtain an explicit expression, in terms of a parabolic cylinder function, for the moment generating function or the characteristic function of x( T) and we evaluate the expected value of x( T).
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