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Comparison results for diffusions conditioned on positivity

Published online by Cambridge University Press:  14 July 2016

Martin V. Day
Martin V. Day*
Affiliation:
Virginia Polytechnic Institute and State University
*
∗ Postal address: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A.
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Abstract

We consider a diffusion process on the reals subject to the conditional probability that the process is positive from t = 0 to the present. We establish comparison results between the conditioned diffusion and a second unconditioned Markov diffusion. One result allows the initial process to be non-Markov before conditioning. A stronger comparison theorem is shown to hold in the Markov case.

Keywords

DIFFUSION PROCESSCONDITIONAL PROBABILITYCOMPARISON THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 766 - 777
Copyright
Copyright © Applied Probability Trust 1983 

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