arXiv subjects

Marwa Masmoudi

Publications and source records attributed to Marwa Masmoudi.

4 recordsLinked to original sources

arXiv2024

A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices

Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the measure free setting of vector lattices (Riesz spaces). We now give a formulation of the Kakutani-Rokhlin decomposition for conditionally ergodic systems in terms of components of weak order units in a vector lattice. In addition, we prove that every aperiodic conditional expectation preserving system can be approximated by a periodic system.

math.DS↗

arXiv2023

Some characterizations of ergodicity in Riesz spaces

In the recent surge of papers on ergodic theory within Riesz spaces, this article contributes by introducing enhanced characterizations of ergodicity. Our work extends and strengthens prior results from both the authors and Homann, Kuo, and Watson. Specifically, we show that in a conditional expectation preserving system (E,T,S,e), S can be extended to the natural domain of T and operates as an isometry on L^{p}(T) spaces.

math.FA↗

arXiv2023

Conditional supremum in Riesz spaces and applications

We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool is crucial in generalizing various results across multiple disciplines to the framework of Riesz spaces. Among other applications, we utilize this concept in finance to derive characterizations of certain financial conditions.

math.FA↗

arXiv2022

The Kac formula and Poincaré recurrence theorem in Riesz spaces

Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional versions of the Poincaré Recurrence Theorem and the Kac formula are developed. Under mild assumptions, it is shown that every conditional expectation preserving process is conditionally ergodic with respect to the conditional expectation generated by the Cesàro mean associated with the iterates of the process. Applied to processes in $L^1(Ω,{\mathcal A},μ)$, where $μ$ is a probability measure, new conditional versions of the above theorems are obtained.

math.PR↗