Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process
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).
Year of publication: |
1989
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Authors: | Lefebvre, Mario |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 32.1989, 2, p. 281-287
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Publisher: |
Elsevier |
Keywords: | first hitting place Ornstein-Uhlenbeck process parabolic cylinder function |
Saved in:
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