×

On first-passage-time and transition densities for strongly symmetric diffusion processes. (English) Zbl 0873.60059

A subclass of symmetric one-dimensional diffusion processes is defined whose transition pdf’s satisfy some “strong” symmetry properties with respect to certain symmetry curves. The purpose is to make use of a variant of the method of images in order to determine a class of time-varying boundaries for which first-passage-time pdf and transition pdf with absorbing conditions on the boundaries can be obtained in closed form for the cases of a single boundary and of a pair of boundaries. New transition pdf’s in the presence of time-dependent boundaries as well as new first-passage-time pdf are thus disclosed. The practical usefulness of these results is pointed out via the derivation of first passage time pdf’s and transition pdf’s in the presence of nontrivial time-varying absorbing boundaries for the hyperbolic process and for the Ornstein-Uhlenbeck process.

MSC:

60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60J60 Diffusion processes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] The Theory of Stochastic Processes (1965)
[2] DOI: 10.2307/1427102 · Zbl 0632.60079 · doi:10.2307/1427102
[3] DOI: 10.2307/3214598 · Zbl 0699.60073 · doi:10.2307/3214598
[4] IEEE Trans. Inform/Theory pp 295– (1973)
[5] In Communications and Networks, A Survey of Recent Advances pp 6– (1986)
[6] DOI: 10.2307/3212009 · Zbl 0209.19702 · doi:10.2307/3212009
[7] J. Appl. Prob 27 pp 707– (1989)
[8] DOI: 10.1090/S0002-9947-1954-0063607-6 · doi:10.1090/S0002-9947-1954-0063607-6
[9] DOI: 10.2307/1969644 · Zbl 0047.09303 · doi:10.2307/1969644
[10] DOI: 10.1214/aos/1176345781 · Zbl 0501.62076 · doi:10.1214/aos/1176345781
[11] DOI: 10.2307/1427196 · Zbl 0668.60068 · doi:10.2307/1427196
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.