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A comparison theorem for conditioned Markov processes

Published online by Cambridge University Press:  14 July 2016

G. O. Roberts
G. O. Roberts*
Affiliation:
University of Nottingham
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate.

The investigation is motivated by applications in estimation of boundary hitting time distributions.

Keywords

BOUNDARY HITTING TIMESTOCHASTICALLY MONOTONEWEAK CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 74 - 83
Copyright
Copyright © Applied Probability Trust 1991 

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