2022/07/25 by Youssef Azouzi, Mohamed Amine Ben Amor, Azouzi, Youssef +7 · 1 citation
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2207.12524
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 L1(Ω,\mathcal A,μ), where μ is a probability measure, new conditional versions of the above theorems are obtained.