Understanding Markov Chains: Examples and Applications (Springer Undergraduate Mathematics Series)

Understanding Markov Chains: Examples and Applications (Springer Undergraduate Mathematics Series)

Nicolas Privault


This booklet presents an undergraduate creation to discrete and continuous-time Markov chains and their functions. a wide concentration is put on step one analysis technique and its functions to general hitting occasions and smash percentages. Classical themes reminiscent of recurrence and transience, desk bound and proscribing distributions, in addition to branching approaches, also are lined. significant examples (gambling approaches and random walks) are taken care of intimately from the start, prior to the overall thought itself is gifted within the next chapters. An advent to discrete-time martingales and their relation to smash chances and suggest go out occasions is usually supplied, and the publication contains a bankruptcy on spatial Poisson strategies with a few fresh effects on second identities and deviation inequalities for Poisson stochastic integrals. The techniques offered are illustrated through examples and via seventy two routines and their whole solutions.

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