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On the inverse of the first hitting time problem for bidimensional processes

  • Mario Lefebvre (a1)

Abstract

Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinitesimal moments that correspond to the chosen moment generating function.

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Postal address: Département de mathématiques et de génie industriel, École Polytechnique, C. P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7.

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Research supported by the Natural Sciences and Engineering Research Council of Canada and by the fund FCAR of Québec.

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References

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On the inverse of the first hitting time problem for bidimensional processes

  • Mario Lefebvre (a1)

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