Bücher der Reihe Probability and Its Applications

This book presents basic properties of self-similar processes, focusing on the study of their variation using stochastic analysis, and also surveys recent techniques and findings on limit theorems and Malliavin calculus.

This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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 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

Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond

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

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

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 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.

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.

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.

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.

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.

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.

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.