Probability Theory - Jurij Anatol'evic Rozanov

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Sommaire:
I Basic Concepts of Elementary Probability Theory.- ? 1. Experiments with Equally Probable Outcomes.- ? 2. The Space of Elementary Events and the Law of Composition of Probabilities.- ? 3. The Relation between Various Events.- ? 4. Random Variables.- ? 5. Some Probability Distributions.- II Spaces and Measures.- ? 1. Some Facts about Measurable and Topological Spaces.- ? 2. Distributions and Measures.- ? 3. Measures and Integrals.- III Basic Concepts of Probability Theory.- ? 1. Spaces of Elementary Events. Probability Distributions and Characteristic Functions.- ? 2. Basic Types of Random Processes.- IV Limit Theorems in Probability Theory.- ? 1. Distributions and their Characteristic Functions.- ? 2. Estimates of the Nearness of Distributions in Terms of the Nearness of their Characteristic Functions.- ? 3. Moments and Semi-Invariants.- ? 4. Infinitely Divisible Distributions and their Connection with Limit Theorems.- ? 5. Sequences of Independent Random Variables (General Properties).- ? 6. Sequences of Independent Random Variables. Convergence to the Normal Law.- ? 7. Sequences of Independent Random Variables. Convergence to Stable Laws.- ? 8. Local Theorems for Lattice-Distributions.- ? 9. Local Theorems for Densities.- ? 10. Probabilities of Large Deviations. Inequalities and Asymptotic Formulas.- ? 11. Concluding Remarks.- V Markov Processes.- ? 1. Markov Processes with a Finite or Denumerable Number of States (Markov Chains).- ? 2. Branching Processes.- ? 3. Random Processes with Independent Increments.- ? 4. Diffusion Processes.- ? 5. General Markov Processes and their Characteristics.- ? 6. Controlled Markov Processes.- VI Stationary Processes.- ? 1. Spectral Theory of Harmonizable Processes.- ? 2. Stationary Processes in theStrict Sense.- ? 3. Stationary Gaussian Processes.- ? 4. Elements of the Mathematical Theory of the Transmission of Information through Stationary Communication Channels.