Resolution of sigma-fields for multiparticle finite-state action evolutions with infinite past

TL;DR

This paper proves that for multiparticle finite-state action evolutions, the observation sigma-field can be decomposed using a third noise generated by a uniform random variable, employing semigroup theory and infinite convolutions.

Contribution

It introduces a novel resolution of the observation sigma-field involving a third noise, combining semigroup theory and infinite convolutions in the context of multiparticle finite-state evolutions.

Findings

Resolution involves a third noise generated by a uniform law

Utilizes Rees decomposition from semigroup theory

Employs theory of infinite convolutions

Abstract

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