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

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  • Lefebvre, Mario

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).

Suggested Citation

  • Lefebvre, Mario, 1989. "Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 281-287, August.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:281-287
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    Cited by:

    1. Lefebvre, Mario, 2024. "Exact solution to a first-passage problem for an Ornstein–Uhlenbeck process with jumps and its integral," Statistics & Probability Letters, Elsevier, vol. 205(C).
    2. Mario Lefebvre, 2003. "First-passage problems for degenerate two-dimensional diffusion processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 125-139, June.
    3. Mario Lefebvre, 2021. "Moments of First-Passage Places for Jump-Diffusion Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 245-253, February.

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