Stochastic Limit Theory

NOTE EDITORE

Stochastic Limit Theory, published in 1994, has become a standard reference in its field. Now reissued in a new edition, offering updated and improved results and an extended range of topics, Davidson surveys asymptotic (large-sample) distribution theory with applications to econometrics, with particular emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First, as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration. The new edition gives updated and improved versions of many of the results and extends the coverage of many topics, in particular the theory of convergence to alpha-stable limits of processes with infinite variance.

SOMMARIO

1 - Sets and Numbers2 - Limits, Sequences, and Sums3 - Measure4 - Integration5 - Metric Spaces6 - Topology7 - Probability Spaces8 - Random Variables9 - Expectations10 - Conditioning11 - Characteristic Functions12 - Stochastic Processes13 - Time Series Models14 - Dependence15 - Mixing16 - Martingales17 - Mixingales18 - Near-Epoch Dependence19 - Stochastic Convergence20 - Convergence in Lp Norm21 - The Strong Law of Large Numbers22 - Uniform Stochastic Convergence23 - Weak Convergence of Distributions24 - The Classical Central Limit Theorem25 - CLTs for Dependent Processes26 - Extensions and Complement27 - Measures on Metric Spaces28 - Stochastic Processes in Continuous Time29 - Weak Convergence30 - Càdlàg Functions31 - FCLTs for Dependent Variables32 - Weak Convergence to Stochastic Integrals

AUTORE

James Davidson is Emeritus Professor of Econometrics at the University of Exeter.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780192844507
• Dimensioni: 236 x 45.0 x 158 mm Ø 1206 gr
• Formato: Brossura
• Pagine Arabe: 816