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A Path Transformation and its Applications to Fluctuation Theory
Author(s) -
Chaumont L.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006929
Subject(s) - transformation (genetics) , path (computing) , extension (predicate logic) , interpretation (philosophy) , mathematics , identity (music) , quantile , path dependent , knight , order (exchange) , statistical physics , mathematical economics , calculus (dental) , computer science , statistics , physics , economics , medicine , dentistry , astronomy , biochemistry , chemistry , finance , acoustics , gene , programming language
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.