Ergodic Markov chains

Information retrieval techniques: Lecture 37. The main topics covered in this chapter include: markov chains; ergodic markov chains; markov chain with teleporting; query processing; personalized pagerank;... Please refer to the content of document.

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This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems. The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach.

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Transient Solution of Markov Chains Transient solution is more meaningful than steady-state solution when the system under investigation needs to be evaluated with respect to its shortterm behavior, Using steady-state measures instead of transient measures could lead to substantial errors in this case. Furthermore, applying transient analysis is the onl y choice if non-ergodic models are investigated, Transient analysis of Markov chains has been attracting increasing attention and is of particular importance in dependability modeling. ...

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Steady-State Solutions of Markov Chains In this chapter, we restrict ourselves to the computation of the steady-state probability vector’ of ergo&c Markov chains. Most of the literature on solution techniques of Markov chains assumes ergodicity of the underlying model. A comprehensive source on algorithms for steady-state solution techniques is the book by Stewart [Stew94]. From Eq. (2.15) and Eq. (2.58), we have v = VP and 0 = nQ, respectively, as points of departure for the study of steady-state solution techniques. Eq. (2.15) can be transformed so that: 0 = Y(P -1).

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