Abstract
Chapter 6 is completely devoted to a discrete time stochastic analysis. It contains the key notions adapted to discrete time like stochastic basis, filtration, predictability, stopping times, martingales, sub- and supermartingales, local densities of probability measures, discrete stochastic integrals and stochastic exponents. It is stated the Doob decomposition for stochastic sequences, maximal inequalities, and other Doob’s theorems. The developed martingale technique is further applied to prove several asymptotical properties for martingales and submartingales (see [1], [7], [8], [10], [15], [40], and [45]).
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