Approximating Matrix-Exponential Distributions by Global Randomization

DOI10.1081/STM-200056231zbMath1070.60013OpenAlexW1977798364MaRDI QIDQ5462812

Armin Heindl, Appie van de Liefvoort

Publication date: 27 July 2005

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/stm-200056231

zbMATH Keywords

uniform convergenceuniformizationmatrix-exponential distributionsdensity/distribution approximationlinear-algebraic approximation

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Probability distributions: general theory (60E05) Approximation by rational functions (41A20) Numerical linear algebra (65F99)

Related Items (3)

Coxian approximations of matrix-exponential distributions ⋮ An Approximation to the Distribution and the Moments of the Number of Events in Markovian Arrival Processes ⋮ On matrix exponential distributions

Cites Work

• Unnamed Item
• Unnamed Item
• The waiting-time distribution and its moments of the PH/PH/1 queue
• Error control of rational approximations to the exponential function
• A numerical study of large sparse matrix exponentials arising in Markov chains.
• The uniformized power method for transient solutions of Markov processes
• Chebyshev rational approximations to \(e^{-x}\) in \([0,+\infty)\) and applications to heat-conduction problems
• Some explicit formulas for the matrix exponential
• The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes
• Approximating Transition Probabilities and Mean Occupation Times in Continuous-Time Markov Chains
• The least variable phase type distribution is erlang
• Some Bounds on the Error in Approximating Transition Probabilities in Continuous-Time Markov Processes
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Erlangian Approximations for Finite-Horizon Ruin Probabilities
• Matrix‐Exponential Distributions: Calculus and Interpretations via Flows

This page was built for publication: Approximating Matrix-Exponential Distributions by Global Randomization