Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Markov property

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_583

When the behavior of a stochastic process {X(t), tT} at times in the future depends only on the present state of the process (past behavior of the process affects the future behavior only through the present state of the process); that is, for any n > 0, any set of time points t1 < t2 <... < tn < tn+1 in the time domain T, and any states x1, x2,..., xn and any set A in the same space, Pr{X(tn+1) ∈ A|X(t1) = x1,..., X(tn) = xn} = Pr{X(tn+1) ∈ A|X(tn) = xn}. Markov chains; Markov processes.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA