Stochastic processes and long range dependence. (2016)

• Record Type: Book
• Further Information: Note: Gennady Samorodnitsky.
• Other Names: Samorodnitsky, Gennady
• Contents: Preface; Contents; 1 Stationary Processes; 1.1 Stationarity and Invariance; 1.2 Stationary Processes with a Finite Variance; 1.3 Measurability and Continuity in Probability; 1.4 Linear Processes; 1.5 Comments on Chapter 1; 1.6 Exercises to Chapter 1; 2 Elements of Ergodic Theory of Stationary Processes and Strong Mixing; 2.1 Basic Definitions and Ergodicity; 2.2 Mixing and Weak Mixing; 2.3 Strong Mixing; 2.4 Conservative and Dissipative Maps; 2.5 Comments on Chapter 2; 2.6 Exercises to Chapter 2; 3 Infinitely Divisible Processes. 3.1 Infinitely Divisible Random Variables, Vectors, and Processes3.2 Infinitely Divisible Random Measures; 3.3 Infinitely Divisible Processes as Stochastic Integrals; 3.4 Series Representations; 3.5 Examples of Infinitely Divisible Self-Similar Processes; 3.6 Stationary Infinitely Divisible Processes; 3.7 Comments on Chapter 3; 3.8 Exercises to Chapter 3; 4 Heavy Tails; 4.1 What Are Heavy Tails? Subexponentiality; 4.2 Regularly Varying Random Variables; 4.3 Multivariate Regularly Varying Tails; 4.4 Heavy Tails and Convergence of Random Measures; 4.5 Comments on Chapter 4. 4.6 Exercises to Chapter 45 Introduction to Long-Range Dependence; 5.1 The Hurst Phenomenon; 5.2 The Joseph Effect and Nonstationarity; 5.3 Long Memory, Mixing, and Strong Mixing; 5.4 Comments on Chapter 5; 5.5 Exercises to Chapter 5; 6 Second-Order Theory of Long-Range Dependence; 6.1 Time-Domain Approaches; 6.2 Spectral Domain Approaches; 6.3 Pointwise Transformations of Gaussian Processes; 6.4 Comments on Chapter 6; 6.5 Exercises to Chapter 6; 7 Fractionally Differenced and Fractionally Integrated Processes; 7.1 Fractional Integration and Long Memory. 7.2 Fractional Integration of Second-Order Processes7.3 Fractional Integration of Processes with Infinite Variance; 7.4 Comments on Chapter 7; 7.5 Exercises to Chapter 7; 8 Self-Similar Processes; 8.1 Self-Similarity, Stationarity, and Lamperti's Theorem; 8.2 General Properties of Self-Similar Processes; 8.3 SSSI Processes with Finite Variance; 8.4 SSSI Processes Without a Finite Variance; 8.5 What Is in the Hurst Exponent? Ergodicity and Mixing; 8.6 Comments on Chapter 8; 8.7 Exercises to Chapter 8; 9 Long-Range Dependence as a Phase Transition; 9.1 Why Phase Transitions? 9.2 Phase Transitions in Partial Sums9.3 Partial Sums of Finite-Variance Linear Processes; 9.4 Partial Sums of Finite-Variance Infinitely Divisible Processes; 9.5 Partial Sums of Infinite-Variance Linear Processes; 9.6 Partial Sums of Infinite-Variance Infinitely Divisible Processes; 9.7 Phase Transitions in Partial Maxima; 9.8 Partial Maxima of Stationary Stable Processes; 9.9 Comments on Chapter 9; 9.10 Exercises to Chapter 9; 10 Appendix; 10.1 Topological Groups; 10.2 Weak and Vague Convergence; 10.3 Signed Measures; 10.4 Occupation Measures and Local Times.
• Publisher Details: Cham : Springer
• Publication Date: 2016
• Extent: 1 online resource (419 pages)
• Subjects: 519.2/3; 510; Mathematics; Stochastic processes; MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Stochastic processes; Mathematics; Probability Theory and Stochastic Processes; Measure and Integration; Dynamical Systems and Ergodic Theory; Mathematics -- Mathematical Analysis; Integral calculus & equations; Nonlinear science; Distribution (Probability theory); Differentiable dynamical systems; Probability & statistics; Electronic books
• Languages: English
• ISBNs: 9783319455754; 3319455753
• Related ISBNs: 9783319455747; 3319455745
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.