Uniform Ergodic Theorems for Regenerative Processes

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 10 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes I, 2025, pp 415-469 from Springer

Abstract: Abstract In Chap. 10 , we consider an infinite family of regenerative processes and present ergodic theorems with explicit power and exponential upper bounds for rates of convergence uniform with respect to this family. We present uniform ergodic theorems for the regenerative processes based on the first and second moments of regeneration times. Then, we present uniform ergodic theorems for the regenerative processes based on the high-order power moments for regeneration times. Finally, we present uniform ergodic theorems for the regenerative processes based on exponential moments for regeneration times.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-89311-7_10

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DOI: 10.1007/978-3-031-89311-7_10

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