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March 2017 Poly-adic filtrations, standardness, complementability and maximality
Christophe Leuridan
Ann. Probab. 45(2): 1218-1246 (March 2017). DOI: 10.1214/15-AOP1085

Abstract

Given some essentially separable filtration $(\mathcal{Z}_{n})_{n\le0}$ indexed by the nonpositive integers, we define the notion of complementability for the filtrations contained in $(\mathcal{Z}_{n})_{n\le0}$. We also define and characterize the notion of maximality for the poly-adic sub-filtrations of $(\mathcal{Z}_{n})_{n\le0}$. We show that any poly-adic sub-filtration of $(\mathcal{Z}_{n})_{n\le0}$ which can be complemented by a Kolmogorovian filtration is maximal in $(\mathcal{Z}_{n})_{n\le0}$. We show that the converse is false, and we prove a partial converse, which generalizes Vershik’s lacunary isomorphism theorem for poly-adic filtrations.

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Christophe Leuridan. "Poly-adic filtrations, standardness, complementability and maximality." Ann. Probab. 45 (2) 1218 - 1246, March 2017. https://doi.org/10.1214/15-AOP1085

Information

Received: 1 July 2014; Revised: 1 December 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 06797090
MathSciNet: MR3630297
Digital Object Identifier: 10.1214/15-AOP1085

Subjects:
Primary: 60J05

Keywords: complementability , Exchange property , Filtrations indexed by the nonpositive integers , maximality , product-type filtrations , Standard filtrations

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • March 2017
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