Generalized inverses and their application to applied probability problems
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In this article, the applicability of generalized inverses to a wide variety of problems in applied probability where a Markov chain is present either directly or indirectly through some form of imbedding is examined.About:
This article is published in Linear Algebra and its Applications.The article was published on 1982-06-01 and is currently open access. It has received 78 citations till now. The article focuses on the topics: Markov renewal process & Discrete phase-type distribution.read more
Citations
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Risk theory in a Markovian environment
TL;DR: In this paper, the authors consider risk processes t t⩾0 with the property that the rate β of the Poisson arrival process and the distribution of B of the claim sizes are not fixed in time but depend on the state of an underlying Markov jump process such that β=β i and B=Bi when Zt=i.
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Asymptotics for steady-state tail probabilities in structured markov queueing models
TL;DR: In this article, the authors apply Tauberian theorems with known transforms to establish asymptotics for the basic steady-state distributions in the BMAP/G/l queue.
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The deviation matrix of a continuous-time markov chain
TL;DR: The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and transition probability matrices P(t) and P(d) is the matrix D ≡ ∫ 0∞(P(t − P) dt as discussed by the authors.
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The role of Kemeny's constant in properties of Markov chains
TL;DR: In a finite irreducible Markov chain with stationary probabilities {π i } and mean first passage times m ij (mean recurrence time when i = ǫ) it was first shown, by Kemeny and Snell (1960), that is a constant, K, (Kemeny's constant) not depending on i.
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Mixing times with applications to perturbed Markov chains
TL;DR: In this paper, the mixing time of a Markov chain was studied and a measure of mixing time in a finite irreducible discrete-time Markov Chain was proposed, where mixing time is defined as the first passage time from state i to state j of the chain.
References
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An Introduction to Probability Theory and Its Applications.
Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
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Finite Markov Chains.
TL;DR: This lecture reviews the theory of Markov chains and introduces some of the high quality routines for working with Markov Chains available in QuantEcon.jl.