Encyclopedia of Operations Research and Management Science

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

Transition probabilities

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_1062

The conditional probabilities describing the movement from state to state of a Markov process {Xt, tT }. In general, the transition probabilities are written as Pr{X(t) ∈ A|X(s) = x} for times s < t in the time domain T and state x and event A in the state space. For a discrete-time Markov chain (DTMC) {Xn,0 ≤ n}, the transition probabilities are Pr{Xn+1 = j|Xn = i} = pij, for time n in the time domain and states i and j in the space state.  Markov chains;  Markov processes.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA