This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.  Meer

Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes...  Meer

This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian.  Meer

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.  Meer

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it 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: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity.  Meer

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.  Meer

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems.  Meer

This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.  Meer

A friendly and systematic introduction to the theory and applications. The book begins with the sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments, which are later used to develop and interpret decoupling inequalities.  Meer

A hundred years ago it became known that deterministic systems can exhibit very complex behavior. By proving that ordinary differential equations can exhibit strange behavior, Poincare undermined the founda­ tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos.  Meer

A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions.  Meer

This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices.  Meer

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas.  Meer

This book is about random objects—sequences, processes, arrays, measures, functionals—with interesting symmetry properties. Here symmetry should beunderstoodinthebroadsenseofinvarianceunderafamily(notnecessarily a group) of measurable transformations.  Meer

"What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences?" In approaching this question a number of probability models are introduced and anyalyzed.  Meer

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.  Meer

This is a substantial expansion of the first edition. The last chapter on stochastic differential equations is entirely new, as is the longish section §9.  Meer

Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. 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.  Meer

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes.  Meer

In this book, 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.  Meer