Resolution of Sigma-Fields for Multiparticle Finite-State Action Evolutions with Infinite Past

Yu Ito, Toru Sera and Kouji Yano ()
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Yu Ito: Kyoto Sangyo University
Toru Sera: Osaka University
Kouji Yano: Kyoto University

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1368-1399

Abstract: Abstract For multiparticle finite-state action evolutions, we prove that the observation $$ \sigma $$ σ -field admits a resolution involving a third noise which is generated by a random variable with uniform law. The Rees decomposition from semigroup theory and the theory of infinite convolutions are utilized in our proofs.

Keywords: Evolution process; Tsirelson’s equation; Resolution of sigma-fields; Third noise; Iteration of random mappings; 60B15; 60F05; 60G50 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01219-4

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