Point processes with finite-dimensional conditional probabilities

DOI10.1016/S0304-4149(99)00006-XzbMath0997.60077OpenAlexW1980516607WikidataQ127663104 ScholiaQ127663104MaRDI QIDQ1613607

Mogens Bladt, Soren Asmussen

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00006-x

zbMATH Keywords

point processesMarkovian arrival processmatrix-exponential distribution

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25)

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A Markov jump process associated with the matrix-exponential distribution ⋮ Quasi-Birth-and-Death Processes with Rational Arrival Process Components ⋮ Markovian Approximations for a Grid Computing Network with a Ring Structure ⋮ Higher Order Moments and Conditional Asymptotics of the Batch Markovian Arrival Process ⋮ Matrix‐Exponential Distributions: Calculus and Interpretations via Flows ⋮ RAP-modulated fluid processes: first passages and the stationary distribution ⋮ From PH/MAP to ME/RAP ⋮ The two-matrix problem ⋮ On properties of the phase-type mixed Poisson process and its applications to reliability shock modeling ⋮ A Markovian canonical form of second-order matrix-exponential processes ⋮ On minimal representations of rational arrival processes ⋮ Characterization of Matrix-Exponential Distributions ⋮ Moment characterization of matrix exponential and Markovian arrival processes ⋮ Joint densities of hitting times for finite state Markov processes ⋮ An alternative characterization for matrix exponential distributions ⋮ On the use of functional calculus for phase-type and related distributions ⋮ Acceptance-Rejection Methods for Generating Random Variates from Matrix Exponential Distributions and Rational Arrival Processes ⋮ Some Structural Properties of Markov and Rational Arrival Processes

Cites Work

• New results on the single server queue with a batch markovian arrival process
• Characterization of phase-type distributions
• A versatile Markovian point process
• The first two moment matrices of the counts for the markovian arrival process
• Marked point processes as limits of Markovian arrival streams
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