The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities

By: Nasa, National Aeronautics and Space Adm

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms. Meyer, C. D., Jr. Unspecified Center NSF MCS-76-11989; NSG-1532

• Format: Paperback
• Language: English
• ISBN: 1720217882
• ISBN13: 9781720217886
• Release Date: January 1
• Publisher: Independently Published
• Length: 28 Pages
• Weight: 0.20 lbs.
• Dimensions: 0.1" x 8.5" x 11.0"