Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process

Mario Lefebvre

Stochastic Processes and their Applications, 1989, vol. 32, issue 2, 281-287

Abstract: We consider the two-dimensional process (x(t),y(t)), where y(t)=dx(t)/dt is an Ornstein-Uhlenbeck process, Let T be the smallest t for which y(t) = [upsilon]. 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).

Keywords: first; hitting; place; Ornstein-Uhlenbeck; process; parabolic; cylinder; function (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (3)

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