Semi-Markov Processes with General State Spaces and Distributional Atoms

Dmitrii Silvestrov
Additional contact information
Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 8 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes II, 2025, pp 299-338 from Springer

Abstract: Abstract In Chap. 8 , we present ergodic theorems with explicit upper bounds for convergence rates for semi-Markov processes with general state spaces and distributional atoms. We introduce regenerative semi-Markov processes with D-distributional atoms with regeneration moments, which are sequential moments of jumps from states in set D, and derive relations that express the distribution functions of its regeneration time and duration of the transition period via the distribution functions of the first hitting times into the set D. Also, necessary and sufficient conditions of finiteness and upper bounds for power and exponential moments of regeneration times, and the duration of the transition period are given in terms of test functions. Finally, we present variants of defining relations for stationary distributions for a semi-Markov process with general state space and distributional atom and its accompanying Markov processes, and ergodic theorems with explicit power and exponential upper bounds for convergence rates for such semi-Markov processes.

Date: 2025
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-89315-5_8

Ordering information: This item can be ordered from
http://www.springer.com/9783031893155

DOI: 10.1007/978-3-031-89315-5_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().