First-passage Problems for Degenerate Two-Dimensional Diffusion Processes

• Autores: Mario Lefebvre
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 12, Nº. 1, 2003, págs. 125-139
• Idioma: inglés
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• Resumen

  • Let Y(t) be a one-dimensional diffusion process and dX(t) = Y(t)dt. The process (X(t),Y(t)) is considered in the second quadrant. First, the probability that (X(t),Y(t)) will hit the x-axis before the y-axis is computed explicitly when Y(t) is a standard Brownian motion or a particular case of the Bessel process. Next, an exact expression is obtained for the average time it takes (X(t),Y(t)) to exit the region C = {(x,y) \in R^2: x < 0, 0 < d1< y < d2 } when Y(t) is a standard Brownian motion. The solution is expressed as a generalized Fourier series.