Stability estimates in the problem of average optimal switching of a Markov chain

Evgueni Gordienko and Alexander Yushkevich

Mathematical Methods of Operations Research, 2003, vol. 57, issue 3, 345-365

Abstract: We consider a switching model for a Markov chain x t with a transition probability p(x|B). The goal of a controller is to maximize the average gain by selecting a sequence of stopping times, in which the controller gets rewards and pays costs (depending on x t ) in an alternating order. We suppose that the exact transition probability function of the original “real” chain x t is not available to the controller, and he/she is forced to rely on a given approximation $\widetildep$ to the unknown p. The controller finds a switching policy $\widetilde\pi$ optimal for the Markov chain with the transition probability $\widetildep$ , with a view to apply $\widetilde\pi$ to the original Markov chain x t . Under certain restrictions on p we give an upper bound for the difference between the maximal gain attainable in switching of x t , and the gain made under the policy in the original model. The bound is expressed in terms of the total variation distance ${{\sup } \over x}{\kern 1pt} {\kern 1pt} {\kern 1pt} Var\left( {p\left( {x\left| \cdot \right.} \right),\widetildep\left( {x\left| \cdot \right.} \right)} \right)$ . Copyright Springer-Verlag Berlin Heidelberg 2003

Keywords: Key words: Positive Harris recurrent chain; average reward; multiple stopping; stability index; total variation metric (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s001860200258 (text/html)
Access to full text is restricted to subscribers.

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:mathme:v:57:y:2003:i:3:p:345-365

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s001860200258

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().