Accession Number : ADA186013
Title : Decoupling Identities and Predictable Transformations in Exchangeability.
Descriptive Note : Technical rept. Sep 86-Sep 87,
Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
Personal Author(s) : Kallenberg, Olav
PDF Url : ADA186013
Report Date : Jun 1987
Pagination or Media Count : 50
Abstract : Let X=(X1,...,Xd) and V=(V1,...,Vd) be processes on (0,1) or R+, such that X is exchangeable while Vd is predictable. Under suitable conditions on X and V, the expression E(pi) Integral over j of (V sub j dX sub j) will only depend on the marginal distributions of X and V. From statements of this type in discrete or continuous time, one may easily derive a variety of old and new results on predictable transformations which preserve the distribution of an exchangeable sequence or process. The same method yields a general result about reduction of continuous local martingales and marked point processes to independent Gaussian and Poisson random fields. Keywords: Stochastic integrals; Product moments; Invariance in distribution; Levy processes; Martingales; Point processes; Brownian bridge; Random time changes.
Descriptors : *BROWNIAN MOTION, *STOCHASTIC PROCESSES, DECOUPLING, IDENTITIES, INTEGRALS, GAUSSIAN QUADRATURE, POISSON DENSITY FUNCTIONS, INVARIANCE, MOMENTS, PREDICTIONS, TRANSFORMATIONS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE