Affordable Access

Access to the full text

Standardness as an invariant formulation of independence

Authors
  • Vershik, A. M.1, 2, 3
  • 1 St. Petersburg Department of Steklov Institute of Mathematics, Moscow, Russia , Moscow (Russia)
  • 2 St. Petersburg State University, Moscow, Russia , Moscow (Russia)
  • 3 Institute for Information Transmission Problems of RAS, Moscow, Russia , Moscow (Russia)
Type
Published Article
Journal
Functional Analysis and Its Applications
Publisher
Springer US
Publication Date
Oct 01, 2015
Volume
49
Issue
4
Pages
253–263
Identifiers
DOI: 10.1007/s10688-015-0114-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

The notion of a homogeneous standard filtration of σ-algebras was introduced by the author in 1970. The main theorem asserted that a homogeneous filtration is standard, i.e., generated by a sequence of independent random variables (is Bernoulli), if and only if a standardness criterion is satisfied. The author has recently generalized the notion of standardness to arbitrary filtrations. In this paper we give detailed definitions and characterizations of Markov standard filtrations. The notion of standardness is essential for applications of probabilistic, combinatorial, and algebraic nature. At the end of the paper we present new notions related to nonstandard filtrations.

Report this publication

Statistics

Seen <100 times