Convergence Property of Standard Transition Functions

Hanjun Zhang, Qixiang Mei, Xiang Lin and Zhenting Hou
Additional contact information
Hanjun Zhang: Changsha Railway University, Research Department
Qixiang Mei: Changsha Railway University, Research Department
Xiang Lin: Changsha Railway University, Research Department
Zhenting Hou: Changsha Railway University, Research Department

Chapter Chapter 4 in Markov Processes and Controlled Markov Chains, 2002, pp 57-67 from Springer

Abstract: Abstract A standard transition function P = (P ij (t)) is called ergodic (positive recurrent) if there exists a probability measure π = (π i ; i ∈ E) such that 0.1 $$ \mathop{{\lim }}\limits_{{t \to \infty }} {{p}_{i}}_{j}(t) = {{\pi }_{j}} > 0,\forall i \in E $$ The aim of this paper is to discuss the convergence problem in (0.1). We shall study four special types of convergence: the so-called strong ergodicity, uniform polynomial convergence, L 2-exponential ergodicity and exponential ergodicity. Our main interest is always to characterize these properties in terms of the q-matrix.

Keywords: strong ergodicity; uniform polynomial convergence; L 2-exponential convergence; exponential ergodicity; stochastic monotonicity (search for similar items in EconPapers)
Date: 2002
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:978-1-4613-0265-0_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461302650

DOI: 10.1007/978-1-4613-0265-0_4

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 ().