1. A new integral equation for the evaluation of first-passage-time probability densities
- Author
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Aniello Buonocore, Luigi Maria Ricciardi, A. G. Nobile, Buonocore, Aniello, A. G., Nobile, and Ricciardi, LUIGI MARIA
- Subjects
Statistics and Probability ,Diffusion equation ,Partial differential equation ,Diffusion Wiener process Ornstein Uhlenbeck process Varying boundaries Daniels boundaries Volterra integral equations ,Applied Mathematics ,Mathematical analysis ,05 social sciences ,050401 social sciences methods ,Summation equation ,Integral equation ,Volterra integral equation ,01 natural sciences ,Stochastic differential equation ,symbols.namesake ,010104 statistics & probability ,0504 sociology ,Integro-differential equation ,Diffusion process ,symbols ,Wiener proce ,Fokker–Planck equation ,0101 mathematics ,Mathematics - Abstract
The first-passage-time p.d.f. through a time-dependent boundary for one-dimensional diffusion processes is proved to satisfy a new Volterra integral equation of the second kind involving two arbitrary continuous functions. Use of this equation is made to prove that for the Wiener and the Ornstein–Uhlenbeck processes the singularity of the kernel can be removed by a suitable choice of these functions. A simple and efficient numerical procedure for the solution of the integral equation is provided and its convergence is briefly discussed. Use of this equation is finally made to obtain closed-form expressions for first-passage-time p.d.f.'s in the case of various time-dependent boundaries.
- Published
- 1987
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