Decoupling Identities and Predictable Transformations in Exchangeability.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1987
- Accession Number
- ADA186013
Entities
People
- Olav Kallenberg
Organizations
- University of North Carolina at Chapel Hill