# Dmitrii Silvestrov: Perturbed Semi-Markov Type Processes

**Time: **
Wed 2022-10-12 15.15 - 16.00

**Location: **
Cramér room, Albano, house 1, floor 3

**Participating: **
Dmitrii Silvestrov (Stockholm University)

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### Abstract

The lecture presents a two-volumes monograph [1, 2], which is devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents phase space reduction algorithms and limit theorems on weak convergence of distributions and convergence of expectations of hitting times for regularly and singularly perturbed semi-Markov processes. These results have their own theoretical and applied significance and also play an important role in obtaining ergodic theorems for perturbed semi-Markov type processes. The second volume presents new super-long-, long- and short-time ergodic theorems for perturbed multi-alternating regenerative processes modulating by regularly or singularly perturbed finite semi-Markov processes. [1] Silvestrov, D.S. Perturbed Semi-Markov Type Processes I. Limit Theorems for Rare-Event Times and Processes, Springer, Cham, 2022, xvii+401 pp. [2] Silvestrov, D.S. Perturbed Semi-Markov Type Processes II. Ergodic Theorems for Multi-Alternating Regenerative Processes, Springer, Cham, 2022, xvii+413 pp.