Probability Theory: Basic Concepts · Limit Theorems Random Processes: Grundlehren der mathematischen Wissenschaften, cartea 157
Autor Jurij Vasil'evic Prohorov Traducere de Klaus Krickeberg Autor Jurij Anatol'evic Rozanov Traducere de H. Urmitzeren Limba Engleză Paperback – 27 mai 2012
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Specificații
ISBN-13: 9783642879364
ISBN-10: 3642879365
Pagini: 420
Ilustrații: XII, 406 p. 20 illus.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.59 kg
Ediția:Softcover reprint of the original 1st ed. 1969
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3642879365
Pagini: 420
Ilustrații: XII, 406 p. 20 illus.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.59 kg
Ediția:Softcover reprint of the original 1st ed. 1969
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
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.