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First-passage times for the Uhlenbeck-Ornstein process

1986; Institute of Physics; Volume: 19; Issue: 17 Linguagem: Inglês

10.1088/0305-4470/19/17/019

1361-6447

Peter W. Duck, Trevor W. Marshall, E. J. Watson,

Nonlinear Dynamics and Pattern Formation

A numerical solution is obtained for the Laplace-transformed backward Kramers equation, from which the mean first-passage time may be obtained. The main difficulties are associated with (a) the parabolic nature of the time-development operator and (b) the existence of a double structure in the solution near the absorbing barrier. Both of these difficulties are resolved by computational methods derived from boundary layer theory. The reliability of the method is assessed by comparing its results with an earlier analytic solution for the case of a uniform force field. The authors also present the results for a harmonic force field, for which no analytic solution is yet known.