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Transition probabilities for some ‘special' diffusions

Published online by Cambridge University Press:  14 July 2016

Václav E. Beneš  and
Ioannis Karatzas
Václav E. Beneš*
Affiliation:
AT&T Bell Laboratories
Ioannis Karatzas*
Affiliation:
Columbia University
*
∗Postal address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
∗∗Postal address: Department of Statistics, Columbia University, New York, NY 10027, USA.
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Abstract

We study the transition probabilities of the diffusions dXt = (1 – exp(Xt))dt + dWt and dXt = – tanh Xtdt + dWt, in terms of special functions of mathematical physics (confluent hypergeometric and Legendre functions, respectively).

Keywords

GIRSANOV THEOREMFEYNMAN–KAC FORMULASPECIAL FUNCTIONS OF MATHEMATICAL PHYSICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 888 - 898
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by the Air Force Office of Scientific Research under grant AFOSR-86-0203.

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