Bøger i Probability and Its Applications serien

This volume covers recent developments in self-normalized processes, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales.

This book presents up-to-date material on the theory of weak convergence of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. Includes exercises.

This will be the most up-to-date book in the area (the closest competition was published in 1990) This book takes a new slant and is in discrete rather than continuous time

This book unifies much research scattered in the literature, and introduces new results first proved by the author. Also presents practical applications, in such highly interesting areas as approximation theory, cosmology and earthquake engineering.

This book presents mathematical techniques for understanding sequence evolution. The theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.

Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games of chance. This book, on the probabilistic aspects of gambling, is a modern version of those classics.

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology. This volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction.

Fully revised and updated by the authors who have reworked their 1988 first edition, this brilliant book brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition.

Mass transportation problems concern the optimal transfer of masses from one location to another. This title is suitable for researchers in applied probability, operations research, computer science, and mathematical economics.

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters.

Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches.

Mass transportation problems concern the optimal transfer of masses from one location to another. This first of two volumes is a useful reference for researchers in applied probability, operations research, computer science, and mathematical economics.

Takes readers in a progressive format from simple to advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems.

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.

A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo­ sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex­ cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems.The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail.

Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. The authors provide the exponential distribution property of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever.

In order to answer Schroedinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations.

This book gives an in-depth description of the structure and basic properties of the following stochastic processes commonly used in applications: Markov chains and continues time, renewal and regenerative processes, Poisson processes and Brownian motion.

Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.

This volume offers comprehensive coverage of modern techniques used for solving problems in infinite dimensional stochastic differential equations. It presents major methods, including compactness, coercivity, monotonicity, in different set-ups.

A hundred years ago it became known that deterministic systems can exhibit very complex behavior. For example, in throwing a die, we can study the limiting behavior of the system by viewing the long-term behavior of individual orbits.

Explains the interplay between probability theory (Markov processes, martingale theory) and operator and spectral theory. This title provides a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes.

Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder.

Applications vary from classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation.

The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

This book is about random objects--sequences, processes, arrays, measures, functionals--with interesting symmetry properties.

Yet again, here is a Springer volume that offers readers something completely new. These examples show how verification theorems and existence theorems may be proved, and that the non-diffusion case is simpler than the diffusion case.