A lovely collection of random and lovely watercolours presented by Robert Ornig.
Kirjahaku
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1000 tulosta hakusanalla Random House Disney
This book provides a well-structured, lyrical, and fictionalized account of the narrator's earlier years in the village of Bialik's birth. It describes the awakening curiosity of the gifted child, his wonder at the riddle of the mirror, and his inability to read the symbols of the alphabet.
This book provides a well-structured, lyrical, and fictionalized account of the narrator's earlier years in the village of Bialik's birth. It describes the awakening curiosity of the gifted child, his wonder at the riddle of the mirror, and his inability to read the symbols of the alphabet.
Random Light Beams: Theory and Applications contemplates the potential in harnessing random light. This book discusses light matter interactions, and concentrates on the various phenomena associated with beam-like fields. It explores natural and man-made light fields and gives an overview of recently introduced families of random light beams. It outlines mathematical tools for analysis, suggests schemes for realization, and discusses possible applications. The book introduces the essential concepts needed for a deeper understanding of the subject, discusses various classes of deterministic paraxial beams and examines random scalar beams. It highlights electromagnetic random beams and matters relating to generation, propagation in free space and various media, and discusses transmission through optical systems. It includes applications that benefit from the use of random beams, as well as the interaction of beams with deterministic optical systems.• Includes detailed mathematical description of different model sources and beams• Explores a wide range of man-made and natural media for beam interaction • Contains more than 100 illustrations on beam behavior• Offers information that is based on the scientific results of the last several years • Points to general methods for dealing with random beams, on the basis of which the readers can do independent researchIt gives examples of light propagation through the human eye, laser resonators, and negative phase materials. It discusses in detail propagation of random beams in random media, the scattering of random beams from collections of scatterers and thin random layers as well as the possible uses for these beams in imaging, tomography, and smart illumination.
The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this emerging area, Random Dynamical Systems in Finance shows how to model RDS in financial applications.Through numerous examples, the book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas.With references at the end of each chapter, this book provides a variety of RDS for approximating financial models, presents numerous option pricing formulas for these models, and studies the stability and optimal control of RDS. The book is useful for researchers, academics, and graduate students in RDS and mathematical finance as well as practitioners working in the financial industry.
In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which relates to the "statistical equilibrium"-and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical analysis and its applications.
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.
Multifractal theory was introduced by theoretical physicists in 1986. Since then, multifractals have increasingly been studied by mathematicians. This new work presents the latest research on random results on random multifractals and the physical thermodynamical interpretation of these results. As the amount of work in this area increases, Lars Olsen presents a unifying approach to current multifractal theory. Featuring high quality, original research material, this important new book fills a gap in the current literature available, providing a rigorous mathematical treatment of multifractal measures.
This book develops appreciation of the ingenuity involved in the mathematical treatment of random phenomena, and of the power of the mathematical methods employed in the solution of applied problems. It is intended to students interested in applications of probability to their disciplines.
This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Random Acts of Medicine: The Hidden Forces That Sway Doctors, Impact Patients, and Shape Our Health
Anupam B. Jena; Christopher Worsham
Doubleday Books
2023
sidottu
Does timing, circumstance, or luck impact your health care? This groundbreaking book reveals the hidden side of medicine and how unexpected--but predictable--events can profoundly affect our health. - Is there ever a good time to have a heart attack? Why do kids born in the summer get diagnosed more often with A.D.H.D.? How are marathons harmful for your health, even when you're not running? "Fantastically entertaining and deeply thought-provoking." --Emily Oster, New York Times bestselling author of The Family Firm, Cribsheet, and Expecting Better "Random Acts of Medicine shows that the ingenious use of natural experiments can improve medicine and save lives." --Wall Street Journal As a University of Chicago-trained economist and Harvard medical school professor and doctor, Anupam Jena is uniquely equipped to answer these questions. And as a critical care doctor at Massachusetts General who researches health care policy, Christopher Worsham confronts their impact on the hospital's sickest patients. In this singular work of science and medicine, Jena and Worsham show us how medicine really works, and its effect on all of us. Relying on ingeniously devised natural experiments--random events that unknowingly turn us into experimental subjects--Jena and Worsham do more than offer readers colorful stories. They help us see the way our health is shaped by forces invisible to the untrained eye. Is there ever a good time to have a heart attack? Do you choose the veteran doctor or the rookie? Do you really need the surgery your doctor recommends? These questions are rife with significance; their impact can be life changing. Addressing them in a style that's both animated and enlightening, Random Acts of Medicine empowers you to see past the white coat and find out what really makes medicine work--and how it could work better.
Random Number Generation and Monte Carlo Methods
James E. Gentle
Springer-Verlag New York Inc.
2003
sidottu
Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.
Random Fields and Geometry
R. J. Adler; Jonathan E. Taylor
Springer-Verlag New York Inc.
2007
sidottu
Since the term “random ?eld’’ has a variety of different connotations, ranging from agriculture to statistical mechanics, let us start by clarifying that, in this book, a random ?eld is a stochastic process, usually taking values in a Euclidean space, and de?ned over a parameter space of dimensionality at least 1. Consequently, random processes de?ned on countable parameter spaces will not 1 appear here. Indeed, even processes on R will make only rare appearances and, from the point of view of this book, are almost trivial. The parameter spaces we like best are manifolds, although for much of the time we shall require no more than that they be pseudometric spaces. With this clari?cation in hand, the next thing that you should know is that this book will have a sequel dealing primarily with applications. In fact, as we complete this book, we have already started, together with KW (Keith Worsley), on a companion volume [8] tentatively entitled RFG-A,or Random Fields and Geometry: Applications. The current volume—RFG—concentrates on the theory and mathematical background of random ?elds, while RFG-A is intended to do precisely what its title promises. Once the companion volume is published, you will ?nd there not only applications of the theory of this book, but of (smooth) random ?elds in general.
Random Effect and Latent Variable Model Selection
Springer-Verlag New York Inc.
2008
nidottu
Random Effect and Latent Variable Model Selection In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of ?elds. For example, it is now standard pr- tice to routinely collect many response variables on each individual in a study. The different variables may correspond to repeated measurements over time, to a battery of surrogates for one or more latent traits, or to multiple types of outcomes having an unknown dependence structure. Hierarchical models that incorporate subje- speci?c parameters are one of the most widely-used tools for analyzing multivariate and correlated data. Such subject-speci?c parameters are commonly referred to as random effects, latent variables or frailties. There are two modeling frameworks that have been particularly widely used as hierarchical generalizations of linear regression models. The ?rst is the linear mixed effects model (Laird and Ware , 1982) and the second is the structural equation model (Bollen , 1989). Linear mixed effects (LME) models extend linear regr- sion to incorporate two components, with the ?rst corresponding to ?xed effects describing the impact of predictors on the mean and the second to random effects characterizing the impact on the covariance. LMEs have also been increasingly used for function estimation. In implementing LME analyses, model selection problems are unavoidable. For example, there may be interest in comparing models with and without a predictor in the ?xed and/or random effects component.
Random Coefficient Autoregressive Models: An Introduction
D.F. Nicholls; B.G. Quinn
Springer-Verlag New York Inc.
1982
nidottu
In this monograph we have considered a class of autoregressive models whose coefficients are random. The models have special appeal among the non-linear models so far considered in the statistical literature, in that their analysis is quite tractable. It has been possible to find conditions for stationarity and stability, to derive estimates of the unknown parameters, to establish asymptotic properties of these estimates and to obtain tests of certain hypotheses of interest. We are grateful to many colleagues in both Departments of Statistics at the Australian National University and in the Department of Mathematics at the University of Wo110ngong. Their constructive criticism has aided in the presentation of this monograph. We would also like to thank Dr M. A. Ward of the Department of Mathematics, Australian National University whose program produced, after minor modifications, the "three dimensional" graphs of the log-likelihood functions which appear on pages 83-86. Finally we would like to thank J. Radley, H. Patrikka and D. Hewson for their contributions towards the typing of a difficult manuscript. IV CONTENTS CHAPTER 1 INTRODUCTION 1. 1 Introduction 1 Appendix 1. 1 11 Appendix 1. 2 14 CHAPTER 2 STATIONARITY AND STABILITY 15 2. 1 Introduction 15 2. 2 Singly-Infinite Stationarity 16 2. 3 Doubly-Infinite Stationarity 19 2. 4 The Case of a Unit Eigenvalue 31 2. 5 Stability of RCA Models 33 2. 6 Strict Stationarity 37 Appendix 2. 1 38 CHAPTER 3 LEAST SQUARES ESTIMATION OF SCALAR MODELS 40 3.
Random Sums and Branching Stochastic Processes
Ibrahim Rahimov
Springer-Verlag New York Inc.
1995
nidottu
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Random Discrete Structures
Springer-Verlag New York Inc.
1995
sidottu
The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for mathematicians and students.