Generalized Ergodic Theorems for Regenerative Processes

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 11 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes I, 2025, pp 471-509 from Springer

Abstract: Abstract In Chap. 10.1007/978-3-031-89311-7_11 , we consider a family of bounded functionals defined on trajectories of a time-shifted regenerative process and present uniform (with respect to this family) ergodic theorems with explicit upper bounds for convergence rates for expectations of these functionals. An important application of these theorems is uniform ergodic theorems for shifted-in-time finite-dimensional distributions of regenerative processes. Also, ergodic theorems with explicit upper bounds for convergence rates are given for thinned regenerative processes.

Date: 2025
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DOI: 10.1007/978-3-031-89311-7_11

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