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First-Passage Distributions of Bidimensional Processes

Published online by Cambridge University Press:  27 July 2009

Mario Lefebvre
Mario Lefebvre
Affiliation:
École Polytechnique de Montréal, Département de Mathématiques et de Génie Industriel, Ecole Polytechnique, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7
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Abstract

Bidimensional processes defined by dx(t) = ρ(x, y) dt and dy(t) = f(y) dt + σ(y) dW(t), where W(t) is a Wiener process, are considered. Let T(x, y, ξ) = inf[t ≥ 0: x(t] = ξ| x(0) = x, y(0) = y). Explicit expressions for the moment generating function of T(x, y, 0) and for the characteristic function of y(T(x, y, ξ)) are obtained in two special cases. The method of similarity solutions is used. Applications to optimal control problems are presented.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 3 , July 1996 , pp. 325 - 339
Copyright
Copyright © Cambridge University Press 1996

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