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When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given.

The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.Concerning the proofs of the limit theorems, the "Fourth Moment Theorem" is systematically used, as it produces rapid and helpful proofs that can serve as models for the future.

Two themes are treated which are closely related to each other and to the law of the iterated logarithm:* I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries.

My interest in majorization was first spurred by Ingram aIkin's proclivity for finding Schur convex functions lurking in the problem section of every issue of the American Mathematical Monthly. The inequality principles of Dalton, especially the transfer or Robin Hood principle, are given appropriate prominence.

This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations.

This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications.

In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently.The test statistics in question range from common ones, such as those used to test e.g.

This book provides a unified introduction to a variety of computational algorithms for Bayesian and likelihood inference. In this third edition, I have attempted to expand the treatment of many of the techniques discussed. I have added some new examples, as well as included recent results. Exercises have been added at the end of each chapter. Prerequisites for this book include an understanding of mathematical statistics at the level of Bickel and Doksum (1977), some understanding of the Bayesian approach as in Box and Tiao (1973), some exposure to statistical models as found in McCullagh and NeIder (1989), and for Section 6. 6 some experience with condi- tional inference at the level of Cox and Snell (1989). I have chosen not to present proofs of convergence or rates of convergence for the Metropolis algorithm or the Gibbs sampler since these may require substantial background in Markov chain theory that is beyond the scope of this book. However, references to these proofs are given. There has been an explosion of papers in the area of Markov chain Monte Carlo in the past ten years. I have attempted to identify key references-though due to the volatility of the field some work may have been missed.

This monograph contains a critical review of 50 years of results on questions of admissibility and minimaxity of estimators of parameters that are restricted to closed convex subsets of Rk . It presents results of approximately 300 mostly-published papers on the subject, and points out relationships between them as well as open problems. The book does not touch on the subject of testing hypotheses for such parameter spaces. It does give an overview of known algorithms for computing maximum likelihood estimators under order-restrictions. The book should be valuable as a reference for researchers and graduate students looking for what is known and unknown in the area of restricted parameter-space-estimation. It assumes a good knowledge of decision theory. Constance van Eeden is Professeur émérite at the Université de Montréal, Honorary Professor at The University of British Columbia, and Professeure associée at the Université du Québec à Montréal. She previously held appointments at the Centrum voor Wiskunde en Informatica (1951-1960), Michigan State University (1960-1961), University of Minnesota (1961-1965), and Université de Montréal (1965-1989). She was a General Editor of Statistical Theory and Method Abstracts (1990-2004) and Associate Editor of the Annals of Statistics (1974-1977), The Canadian Journal of Statistics (1980-1994) and Annales des sciences mathématiques du Québec (1986-1998). She is a reviewer for Mathematical Reviews and a member of the Noether Award Committee. The Statistical Society of Canada awarded her their Gold Medal in 1990 and the Département de mathématiques et de statistique at the Université de Montréal named their yearly prize for the best-finishing undergraduate student in actuarial studies or statistics, the Prix Constance-van-Eeden. She is a Fellow of the Institute of Mathematical Statistics and of the AmericanStatistical Association, and an Elected Member of the International Statistical Institute. She (co-)authored 66 papers in refereed journals, as well as two books and (co-)supervised 14 PhD and 19 MSc students.

I. Additives Which Modify Physical Properties.- 1 Plasticizers.- 1.1 Thermodynamic Basis of Macromolecular Mixtures.- 1.1.1 Solubility of Polymers in Solvents.- 1.1.2 Flory-Huggins Interaction Parameter.- 1.1.3 Solubility Parameter.- 1.1.4 Phase Separation Phenomena.- 1.2 Reversible Gelation.- 1.3 Theory of Plasticization.- 1.3.1 Effect of Plasticizers on Thermal Mechanical Deformation of Rigid Polymeric Chains.- 1.3.2 Effect of Plasticizers on Tb and Tg Values.- 1.3.3 The Free Volume in Amorphous Polymers.- 1.3.4 Primary and Secondary Plasticizers.- 1.4. Classification of Plasticizers.- 1.4.1 Polar Aromatic and Polar Aliphatic Plasticizers.- 1.4.2 Characteristics of Plasticizers According to Their Chemical Structure.- 1.5. Plasticizer Anomalies and Antiplasticization.- 1.6. Loss of Plasticizers.- References.- 2 Lubricants and Mold-Release Agents.- 2.1 Lubricants.- 2.1.1 Principles of Their Action.- 2.1.2 Classification of PVC Lubricants According to Their Specific Action.- 2.1.3 Classification of PVC Lubricants According to Their Chemical Structure.- 2.1.4 Lubricants for Polyolefins.- 2.1.5 Basic Properties Necessary for Lubricants.- 2.2 Mold-Release Agents.- 2.2.1 Principles of Action.- 2.2.2 Some Examples of Mold-Release Agents.- References.- 3 Macromolecular Modifiers.- 3.1 Introduction.- 3.2 Homogenization of Polymer-Polymer Systems.- 3.3 Two-Phase Microheterogeneous Polymer-Polymer Systems.- 3.3.1 Effect of Glassy Polymer Matrix Phase on Impact Strength.- 3.3.2 Effect of Rubbery Phase Dispersed in Glassy Matrix on Impact Strength.- 3.3.3 Theory on Toughness of Microheterogeneous Two-Phase Polymer-Polymer Blends.- 3.4 Impact Modifiers for Glassy Polymers.- 3.4.1 Chlorinated Polyethylene (CPE).- 3.4.2 Ethylene-(Vinyl Acetate) Copolymers (EVA).- 3.4.3 Acrylic and Methacrylic Elastomers and MBS and ABS Terpolymers.- 3.4.4 Rubbers.- 3.5 Macromolecular Modifiers Used as Polymer Processing Aids.- References.- 4 Reinforcing Fillers, Reinforcing Agents, and Coupling Agents.- 4.1 Fillers.- 4.1.1 General Characteristics of Fillers and Composites.- 4.1.2 Fillers for Thermosetting Resins.- 4.1.3 Fillers for Plastomers.- 4.1.3.1 Polymer Reinforcement Factors.- 4.1.3.2 Classification of Fillers for Plastomers According to Their Reinforcement Activity.- 4.2 Reinforcing Agents for Laminates.- 4.2.1 Effect of Fillers or Reinforcing Agents on Basic Physical Properties of Composites.- 4.3 The Different Types of Fillers and Reinforcing Agents.- 4.3.1 Glass Fillers and Reinforcing Agents.- 4.3.1.1 Glass Fibers.- 4.3.1.2 Glass Microspheres.- 4.3.1.3 Glass Flakes.- 4.3.2 Fillers and Reinforcing Agents Made of Other Materials.- 4.3.2.1 Fibrous and Flaky Fillers and Fibrous Reinforcing Agents.- 4.3.2.2 Whiskers, Microfibers, and Powdered Fillers.- 4.3.3 Effect of Content and Size of Fillers on Composite Properties.- 4.4 Coupling Agents.- 4.4.1 Silane Coupling Agents.- 4.4.1.1 Action Mechanism.- 4.4.2 Organotitanate Coupling Agents.- 4.4.2.1 Action Mechanism.- 4.4.3 Other Types of Coupling Agents.- 4.4.4 Application Modes for Coupling Agents.- 4.4.5 Recommendations on the Use of Fillers and Filling Methods.- References.- 5 Colorants and Brightening Agents.- 5.1 Colorants.- 5.1.1 Inorganic Pigments.- 5.1.2 Organic Pigments.- 5.1.3 Criteria for Selection of Pigments.- 5.2 Brightening Agents.- 5.3 Methods Used for the Coloration of Plastics.- 5.3.1 Some Examples of Methods Used for the Coloration of Most Important Plastics.- References.- 6 Chemical and Physical Blowing Agents.- 6.1 Chemical Blowing Agents.- 6.1.1 Inorganic Agents.- 6.1.2 Organic Agents.- 6.1.2.1 Characteristics.- 6.1.3 Factors Acting on Blowing.- 6.2 Physical Blowing Agents.- References.- 7 Antistatic Agents.- 7.1 Introduction.- 7.2 Efficiency and Mechanism of Antistatic Agent Action.- 7.3 The Use of Antistatic Agents.- 7.3.1 Antistatic Agents Containing Nitrogen.- 7.3.2 Antistatic Agents Containing Phosphorus.- 7.3.3 Antistatic Agents Containing Sulfur.- 7.3.4 Betaine-Type Antist...

1.1 Rationale.- 1.2 An Overview.- Soil Acidification: Fundamental Concepts.- The Sulfur System.- 3.1 The Sulfate Cycle.- 3.2 Sulfate Adsorption.- 3.3 The Biotic Component.- 3.4 Summary.- The Nitrogen System.- 4.1 Acid-Base Relationships of the Nitrogen Cycle.- 4.2 Acid-Base Relationships of Nitrogen Inputs.- 4.3 Ecosystem Effects.- Soil-Solution Interactions.- 5.1 Role of Anions.- 5.2 Ion Equilibria Model.- 5.3 Conceptualizing the Model.- 5.4 Solution Concentration Effects.- 5.5 Cation Removal, ?M/?H.- 5.6 Complexes and Precipitates.- 5.7 Organic Anions.- 5.8 Summary.- Forest Element Cycling.- 6.1 Definition of Terms.- 6.2 Effects of Acid Deposition on Base Cation Flux.- 6.3 Cation Nutrient Effects.- The Aquatic Interface.- 7.1 Alkalinity Concepts.- 7.2 Alkalinity in Soil Solution.- 7.3 Naturally Acid Waters.- 7.4 Sensitivity to Water Acidification.- 7.5 Capacity versus Intensity.- Soil Sensitivity.- Base Cation Depletion.- Sensitivity to pH Changes.- Sensitivity to Aluminum Mobilization.- Summary.- Conclusion.- 9.1 Summary.- 9.2 Concepts in Transition.- References.- Appendix: Model Documentation.- A.1 Model Description.- A.2 Program Operation.- A.3 Program Documentation.- A.4 Program Listings.

This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.