Semi‐Markov Processes

A semi‐Markov process is a generalization of continuous‐time Markov chain, so that the sojourn times come from general distributions. In this article, after some basic definitions, some results related to the transient and limiting properties of the semi‐Markov processes are given. Some results are demonstrated with examples.


Joint densities of hitting times for finite state Markov processes
Bielecki, Tomasz R.; Jeanblanc, Monique; Sezer, Ali Devin (2018-01-01)
For a finite state Markov process X and a finite collection {Gamma<INF>k</INF>, k is an element of K} of subsets of its state space, let tau<INF>k</INF> be the first time the process visits the set Gamma<INF>k</INF>. In general, X may enter some of the Gamma<INF>k</INF> at the same time and therefore the vector tau := (tau<INF>k</INF>, k is an element of K) may put nonzero mass over lower dimensional regions of R<INF>+</INF> <SUP>vertical bar K vertical bar</SUP>;these regions are of the form R<INF>s</INF> ...
A High throughput FPGA implementation of markov chain monte carlo method for mixture models
Bozgan, Caner; Ulusoy, İlkay; Department of Electrical and Electronics Engineering (2019)
Markov Chain Monte Carlo (MCMC) is a class of algorithms which can generate samples from high dimensional and multimodal probability distributions. In many statistical and control applications, MCMC algorithms are employed widely thanks to their ability to draw sample from arbitrary distribution regardless of dimension or complexity. However, as the complexity of the Bayesian models and the computational load of the MCMC algorithm increase, performing MCMC inference becomes impractical or too time consuming...
Non-simply connected Calabi-Yau threefolds constructed as quotients of Schoen threefolds
Karayayla, Tolga (2017-07-01)
The aim of this paper is to complete the classification of all Calabi-Yau threefolds which are constructed as the quotient of a smooth Schoen threefold X = B-1 x p1 B-2 (fiber product over P-1 of two relatively minimal rational elliptic surfaces B-1 and B-2 with section) under a finite group action acting freely on the Schoen threefold X. The abelian group actions on smooth Schoen threefolds which induce cyclic group actions on the base curve P-1 were studied by Bouchard and Donagi (2008), and all such acti...
Approximation of the exit probability of a stable Markov modulated constrained random walk
Kabran, Fatma Basoglu; Sezer, Ali Devin (2020-06-01)
Let X be the constrained randomwalk on Z(+)(2) having increments (1, 0), (- 1, 1), (0,- 1) with jump probabilities lambda(M-k), mu(1)(M-k), and mu(2)(M-k) where M is an irreducible aperiodic finite state Markov chain. The process X represents the lengths of two tandem queues with arrival rate lambda(M-k), and service rates mu(1)(M-k), and mu(2)(M-k); the process M represents the random environment within which the system operates. We assume that the average arrival rate with respect to the stationary measur...
On a class of non-simply connected Calabi-Yau 3-folds with positive Euler characteristic
Karayayla, Tolga (2022-01-01)
In this work we obtain a class of non-simply connected Calabi-Yau 3-folds with positive Euler characteristic as the quotient of projective small resolutions of singular Schoen 3-folds under the free action of finite groups. A Schoen 3-fold is a fiber product X = B-1 x(P1) B-2 of two relatively minimal rational elliptic surfaces with section beta(i) : B-i -> P-1, i = 1, 2. Schoen has shown that if X is smooth, then X is a simply connected Calabi-Yau 3-fold, and if the only singularities of X are on I-r x I-s...
Citation Formats
Y. Y. Serin, Semi‐Markov Processes. 2010.