Strong approximation theorems for density dependent Markov chains

Thomas G. Kurtz

Stochastic Processes and their Applications, 1978, vol. 6, issue 3, 223-240

Abstract: A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where l[set membership, variant]Zt, the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution). The corresponding deterministic model, satisfies X(t)=x0+ [integral operator]t0 [summation operator] lf1(X(s))ds Under very general conditions limN-->[infinity]XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and

Date: 1978
References: Add references at CitEc
Citations: View citations in EconPapers (28)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(78)90020-0
Full text for ScienceDirect subscribers only

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:eee:spapps:v:6:y:1978:i:3:p:223-240

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().