Titlebook: Discrete Probability Models and Methods; Probability on Graph Pierre Brémaud Textbook 2017 Springer International Publishing Switzerland 20

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Martingale Methods,crease or decrease (the precise definition will be given soon). This notion has to do with casino games but it is also useful outside Las Vegas. In fact, it is one of the foundations of modern probability theory.

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The probabilistic Method,ollection of tricks, but as one gets used to it, some unity emerges from the recurrence of these tricks that henceforth deserve to be called “tools”. One can of course strive to give a unified theoretical treatment to the probabilistic method.

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The Method of Types, in the continuous case require a rather formidable technical equipment: Sanov’s principle and the maximum entropy principle. The objects considered by this method are empirical averages, and the basic mathematical notion is that of divergence.

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Universal Source Coding,vironment, they loose their optimality (see Example 13.1.1). One is therefore led to investigate the existence of codes that are less, and hopefully not, sensitive to the source statistics. These codes are called universal. The following example gives an idea of what can be expected.

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Martingale Methods,crease or decrease (the precise definition will be given soon). This notion has to do with casino games but it is also useful outside Las Vegas. In fact, it is one of the foundations of modern probability theory.

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