Differential equation approximations for Markov chains

被引：145

作者：

Darling, R. W. R. ^{[1
]}

Norris, J. R. ^{[2
]}

机构：

[1] Natl Secur Agcy, Math Res Grp, 9800 Savage Rd, Ft George G Meade, MD 20755 USA

[2] Univ Cambridge, Stat Lab, Ctr Math Sci, Cambridge CB3 0WB, England

来源：

PROBABILITY SURVEYS | 2008年 / 5卷

关键词：

D O I：

10.1214/07-PS121

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is emphasised. The general theory is illustrated in three examples: the classical stochastic epidemic, a population process model with fast and slow variables, and core-finding algorithms for large random hypergraphs.

引用

页码：37 / 79

页数：43

共 21 条

[1] Lower bounds for random 3-SAT via differential equations [J].

Achlioptas, D .

THEORETICAL COMPUTER SCIENCE, 2001, 265 (1-2) :159-185

[2] Asymptotic analysis of multiscale approximations to reaction networks [J].

Ball, Karen ;

Kurtz, Thomas G. ;

Popovic, Lea ;

Rempala, Greg .

ANNALS OF APPLIED PROBABILITY, 2006, 16 (04) :1925-1961

[3]

Daley D., 1999, CAMBRIDGE STUDIES MA, V15

[4]

Darling R. W. R., 2008, CORES CYCLES RANDOM

[5]

Ethier S.N., 1986, WILEY SERIES PROBABI, DOI DOI 10.1002/9780470316658

[6]

Hajek B., 1988, Proceedings of the 27th IEEE Conference on Decision and Control (IEEE Cat. No.88CH2531-2), P1455, DOI 10.1109/CDC.1988.194566

[7]

JACOD J, 2003, GRUNDLEHREN MATH WIS, DOI DOI 10.1007/978-3-662-05265-5

[8]

KALLENBERG O., 2002, FDN MODERN PROBABILI, V2nd, DOI 10.1007/978-1-4757-4015-8

[9]

Karp R. M., 1981, 22nd Annual Symposium on Foundations of Computer Science, P364, DOI 10.1109/SFCS.1981.21

[10]

KURTZ TG, 1981, CBMS NSF REGIONAL C, V0036

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