The transition pdf for a one-dimensional Rayleigh process in the presence of an absorbing condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time pdf is explicitly derived. Use of some of these results is finally made to obtain the transition pdf of the affine drift-linear -infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition
Some remarks on the Rayleigh process
GIORNO, Virginia;NOBILE, Amelia Giuseppina;
1986-01-01
Abstract
The transition pdf for a one-dimensional Rayleigh process in the presence of an absorbing condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time pdf is explicitly derived. Use of some of these results is finally made to obtain the transition pdf of the affine drift-linear -infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection conditionFile in questo prodotto:
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