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A PATH TRANSFORMATION AND ITS APPLICATIONS TO FLUCTUATION THEORY

Published online by Cambridge University Press:  01 April 1999

L. CHAUMONT
L. CHAUMONT
Affiliation:
Laboratoire de Probabilités, Tour 56, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Abstract

We first establish a combinatorial result on deterministic real chains. This is then applied to prove a path transformation for chains with exchangeable increments. From this transformation we derive an identity on order statistics due to Port, together with some extensions. Then we give an interpretation of these results in continuous time. We extend some identities involving quantiles and occupation times for processes with exchangeable increments. In particular, this yields an extension of the uniform law for bridges obtained by Knight.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 729 - 741
Copyright
The London Mathematical Society 1999

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