On Standardness and I-cosiness

DOI10.1007/978-3-642-15217-7_5zbMath1230.60035OpenAlexW1668301538MaRDI QIDQ3086796

Stéphane Laurent

Publication date: 30 March 2011

Published in: Séminaire de Probabilités XLIII (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-15217-7_5

zbMATH Keywords

\(\sigma\)-algebrafiltrationstandardnesscosinessbackward filtrationRosenblatt's joining conditionself-joining of a filtrationsplit-word processes.Vershik's first level criterionVershik's joining conditionVershik's standardness criterion

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Probability measures on topological spaces (60B05) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Foundations of stochastic processes (60G05)

Related Items (12)

Classification of backward filtrations and factor filtrations: examples from cellular automata ⋮ SDEs with no strong solution arising from a problem of stochastic control ⋮ The theory of filtrations of subalgebras, standardness, and independence ⋮ Non-extremal martingale with Brownian filtration ⋮ The filtration of the split-words process ⋮ Complementability and Maximality in Different Contexts: Ergodic Theory, Brownian and Poly-Adic Filtrations ⋮ Uniform Entropy Scalings of Filtrations ⋮ Filtrations at the threshold of standardness ⋮ Further comments on the representation problem for stationary processes ⋮ Filtrations associated to some two-to-one transformations ⋮ Vershik’s Intermediate Level Standardness Criterion and the Scale of an Automorphism ⋮ Filtrations of the Erased-Word Processes

Cites Work

• The filtration of the split-words process
• Four definitions of the scale of an automorphism
• On the invariance principle for sums of independent identically distributed random variables
• Bernoullis are standard when entropy is not an obstruction
• Processes with no standard extension
• Triple points: From non-Brownian filtrations to harmonic measures
• On certain almost Brownian filtrations
• Continuum of pairwise nonisomorphic dyadic sequences
• Decreasing sequences of \(\sigma\)-fields and a measure change for Brownian motion. I
• On Vershikian and I-Cosy Random Variables and Filtrations
• Foundations of Modern Probability
• Decreasing sequences of measurable partitions: product type, standard and prestandard
• Addendum to our paper ‘Decreasing sequences of sigma fields: product type, standard, and substandard’
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