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References [1] Barlow R. E., Proshan F., Statistical theory of reliability and life testing, Holt, Rinchart and Winston, Inc., New York 1975. [2] Cinlar E., Markov renewal theory, ‘Adv. Appl. Probab.’, 1969, No. 1, pp. 123-187. [3] Feller W., On semi-Markov processes, ‘Proc. Nat. Acad. Sci.’, 1964, Vol. 51, No. 4, pp. 653-659. [4] Grabski F., Theory of Semi-Markov Operation Processes, ‘Zeszyty Naukowe AMW’, 1982, 75A [in Polish]. [5] Grabski F., Semi-Markov models of reliability and operation, IBS PAN, Warsaw 2002 [in Polish]. [6] Grabski F., Semi-Markov

. In: The Fifth International IEEE Conference on Quantitative Evaluation of Systems, (2008), pp 215–224. [12] C. Bordenave, D. McDonald, A. Proutiere, A particle system in interaction with a rapidly varying environment: Mean-field limits and applications, Networks and Heterogeneous Media, 5(1) (2010) 31–62. [13] K.A. Borovkov, Propagation of chaos for queueing networks, Theory of Probability & Its Applications, 42(3) (1998) 385–394. [14] A. Bovier, Markov processes and metastability, Lecture Notes TUB, (2003), pp 1–75. [15] A. Bovier, Metastability: A potential

Volume 3, Issue 4 2007 Article 4 Journal of Quantitative Analysis in Sports Position Play in Carom Billiards as a Markov Process Mathieu Bouville, Institute of Materials Research and Engineering Recommended Citation: Bouville, Mathieu (2007) "Position Play in Carom Billiards as a Markov Process," Journal of Quantitative Analysis in Sports: Vol. 3: Iss. 4, Article 4. DOI: 10.2202/1559-0410.1075 ©2007 American Statistical Association. All rights reserved. Position Play in Carom Billiards as a Markov Process Mathieu Bouville Abstract Position play is a key feature

, 41 N° RR-17: 1-19 Corradi G., Janssen J., Manca R. (2004):Numerical treatment of homogeneous semi- Markov processes in transient case-a straightforward approach. Methodology and Computing in Applied Probability 6: 233-246. D’Amico G., Di Biase G., Janssen J., Manca R. (2011):HIV Evolution: A Quantification of the Effects Due to Age and to Medical Progress. Informatica 22 (1): 27-42. Davidov O. (1999): The steady state probabilities for a regenerative semi-Markov processes with application to prevention and screening. Applied Stochastic Models and Data Analysis 15

Statistics & Decisions 28, 151–168 (2011) / DOI 10.1524/stnd.2011.1068 c© Oldenbourg Wissenschaftsverlag, München 2011 Comparison of Markov processes via infinitesimal generators Ludger Rüschendorf, Viktor Wolf Received: May 19, 2010; Accepted: January 12, 2011 Summary: We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no

Theory and Applications to Biology

Chapter Four Markov Processes In this chapter, we begin our study of Markov processes, which in turn lead to “hidden” Markov processes, the core topic of the book. We define the “Markov property,” and show that all the relevant information about a Markov process assuming values in a finite set of cardinality n can be captured by a nonnegative n×n matrix called the “state transition matrix,” and an n-dimensional probability distribution of the initial state. Then we invoke the results of Chapter 3 on nonnegative matrices to analyze the temporal evolution of Markov

LECTURE 19 MARKOV PROCESSES Let us consider a probability space (fí,¡?, P) containing a filtration {5t,t > 0}, that is, an increasing with t family of a-algebras. A cr-algebra is treated as a family of events observed up to the moment t. A stochastic process x(t,u) with a phase space (X , 93) is said to be a Markov random function in a wide sense if it is adapted to a filtration {5(} and for all B € 93 and s < t P (x(t,U) € B / 5 . ) = P (x(t,W) £ B/X(S,LJ)) . (1) The expression on the right hand side of (1) is a measurable function of X(S,UJ) and is

Chapter 3 Markov processes In this chapter, we construct a Hunt process corresponding to a regular Dirichlet form. In Section 3.1, we shall state some general properties of Hunt processes. In particular, some basic properties of excessive functions are shown in Section 3.2. For a regular Dirichlet form, by choosing a suitable modification ¹R˛º of the resolvent ¹G˛º and using the Ray process corresponding to it, we construct in Section 3.3 a Hunt process associated with the Dirichlet form. Although the dual Hunt process does not exist in general, by changing the

GEORGIAN MATHEMATICAL JOURNAL: Vol. 2, No. 4, 1995, 335-346 ON OPTIMAL STOPPING OF INHOMOGENEOUS STANDARD MARKOV PROCESSES B. DOCHVIRI Abstract. The connection between the optimal stopping problems for inhomogeneous standard Markov process and the corresponding homogeneous Markov process constructed in the extended state space is established. An excessive characterization of the value-function and the limit procedure for its construction in the problem of optimal stopping of an inhomogeneous standard Markov process is given. The form of ε-optimal (optimal