A PATH TRANSFORMATION AND ITS APPLICATIONS TO FLUCTUATION THEORY

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 interpre...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 1999-04, Vol.59 (2), p.729-741
Main Author: CHAUMONT, L.
Format: Article
Language:English
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Summary: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/S0024610798006929