Structural Decomposition of Multiple Time Scale Markov Processes,

Abstract

A straightforward algorithm for the multiple time scale decomposition of singularly perturbed Markov processes has been presented. That algorithm provides a uniform approximation of the probability transition function over the interval t > or = 0 through the construction of a sequence of aggregate models valid at successively slower time scales. When only the structure of these models is desired, the algorithm can be expressed simply in terms of graphs associated with each of the aggregated models. The major computation then becomes computing shortest paths in these graphs. This representation of the algorithm furthermore allows analysis of more complex systems where there are multiple perturbation parameters with unknown relative orders of magnitude. Keywords: Markov processes; Singular perturbation; Multiple time scales; Graph theory.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1987
Accession Number
ADA189739

Entities

People

  • A. S. Willsky
  • J. R. Rohlicek

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Complex Systems
  • Computations
  • Decomposition
  • Generators
  • Iterations
  • Markov Chains
  • Markov Processes
  • Military Research
  • Models
  • Probability
  • Scale Models
  • Sequences
  • Standards
  • Transitions

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.