Doeblin and Modern Probability.

Intro -- Contents -- Preface -- Introduction -- Doeblin's Life and Work -- Doeblin's life and work from his correspondence -- Reminiscences of one of Doeblin's papers -- Coupling -- The coupling technique in interacting particle systems -- Coupling and shift-coupling random sequences -- Continued Fractions and Ergodicity -- Doeblin and the metric theory of continued fractions: A functional theoretic solution to Gauss' 1812 problem -- A basic tool in mathematical chaos theory: Doeblin and Fortet's ergodic theorem and Ionescu Tulcea and Marinescu's generalization -- The nearest integer continued fraction expansion: An approach in the spirit of Doeblin -- Independent and Weakly Dependent Random Variables -- On the weighted asymptotics of partial sums and empirical processes of independent random variables -- Homoclinic approach to the central limit theorem for dynamical systems -- Asymptotic results for φ-mixing sequences -- The central limit theorem and Markov sequences -- Homogeneous and Non-homogeneous Markov Chains -- Behaviour of infinite products with applications to non-homogeneous Markov chains -- Applications of ergodicity coefficients to homogeneous Markov chains -- Markov Processes -- Applications of some constructions of Markov processes -- The Doeblin decomposition -- Generalized resolvents and Harris recurrence of Markov processes -- Stochastic and Nonstochastic Matrices -- Majorization, monotonicity of relative entropy, and stochastic matrices -- Products of stochastic, nonstochastic, and random matrices -- Shuffling with two matrices -- Stochastic Processes -- Continuous time gambling problems -- Stochastic processes with long range interactions of the paths -- Some remarks on products of random affine maps on (R+)d -- A multivariate look at E. Sparre Andersen's equivalence principle.

Regeneration for chains of infinite order and random maps.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.