Titlebook: Understanding Markov Chains; Examples and Applica Nicolas Privault Textbook 20131st edition Springer Nature Singapore Pte Ltd. 2013 Applica

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Discrete-Time Martingales,results on gambling processes of Chapter?.. Before that, let us state many recent applications of stochastic modeling are relying on the notion of martingale. In financial mathematics for example, the notion of martingale is used to characterize the fairness and equilibrium of a market model.

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Probability Background,refer to Devore (Probability and Statistics for Engineering and the Sciences. Duxbury Press, sixth edition, .), Jacod and Protter (Probability Essentials. Springer, .), and Pitman (Probability. Springer, .) for additional probability material.

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Gambling Problems,te state space {0,1,…,.}. This allows us in particular to have a first look at the technique of first step analysis that will be repeatedly used in the general framework of Markov chains, particularly in Chapter?..

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Continuous-Time Markov Chains, from discrete to continuous-time Markov chains, the main difference between the two settings being the replacement of the transition matrix with the continuous-time . of the process. We will start with the two fundamental examples of the Poisson and birth and death processes, followed by the constr

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Spatial Poisson Processes,se . is the real half line, these random points can be identified with the jump times (. .). of the standard Poisson process . introduced in Section?.. However, in contrast with the previous chapter, no time ordering is . imposed here on the index set .. Sections?. and . contain some more advanced r

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Textbook 20131st edition first step analysis?technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) a