Bücher der Reihe Probability and Its Applications

Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae.

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.

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance.

The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hoermander's sum of squares theorem but has found a range of applications in stochastic analysis.

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.

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.

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.

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.

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 book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration.

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 self-contained introduction to the dynamic martingale approach to marked point processes (MPP).

Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond

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

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.

Covering an active and high-profile research topic, this volume presents a unified, rigorous treatment of recent developments in control theory that unlock numerous applications in high-integrity systems such as robotics, economics and wireless communications.

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.

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 title is suitable for researchers in applied probability, operations research, computer science, and mathematical economics.

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.

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.

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.

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.

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.

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.

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.

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 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.