We study an inverse first-hitting problem for a one-dimensional, time-homogeneous diffusion X(t) reflected between two boundaries a and b, which starts from a random position η. Let a ≤ S ≤ b be a given threshold, such that P(η [a, S]) = 1, and F an assigned distribution function. The problem consists of finding the distribution of η such that the first-hitting time of X to S has distribution F. This is a generalization of the analogous problem for ordinary diffusions, that is, without reflecting, previously considered by the author.
Abundo, M.r. (2014). One-dimensional reflected diffusions with two boundaries and an inverse first- hitting problem. STOCHASTIC ANALYSIS AND APPLICATIONS, 32, 975-991 [10.1080/07362994.2014.959595].
One-dimensional reflected diffusions with two boundaries and an inverse first- hitting problem.
ABUNDO, MARIO ROSOLINO
2014-01-01
Abstract
We study an inverse first-hitting problem for a one-dimensional, time-homogeneous diffusion X(t) reflected between two boundaries a and b, which starts from a random position η. Let a ≤ S ≤ b be a given threshold, such that P(η [a, S]) = 1, and F an assigned distribution function. The problem consists of finding the distribution of η such that the first-hitting time of X to S has distribution F. This is a generalization of the analogous problem for ordinary diffusions, that is, without reflecting, previously considered by the author.File | Dimensione | Formato | |
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