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

Author

Listed:
  • Yu Ito

    (Kyoto Sangyo University)

  • Toru Sera

    (Osaka University)

  • Kouji Yano

    (Kyoto University)

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.

Suggested Citation

  • Yu Ito & Toru Sera & Kouji Yano, 2023. "Resolution of Sigma-Fields for Multiparticle Finite-State Action Evolutions with Infinite Past," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1368-1399, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01219-4
    DOI: 10.1007/s10959-022-01219-4
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    References listed on IDEAS

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    1. Kouji Yano, 2013. "Random Walk in a Finite Directed Graph Subject to a Road Coloring," Journal of Theoretical Probability, Springer, vol. 26(1), pages 259-283, March.
    2. Hirayama, Takao & Yano, Kouji, 2010. "Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1404-1423, August.
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