The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris.
The seventh International Conference on Evolution Equations and their main areas of Applications (where the emphasis evolves as time and problems change) was held October 30 to November 4 at the CIRM (Centro Internazionale per la Ricerca Matematica) in Trento, Italy.
Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics.
The title High Dimensional Probability is an attempt to describe the many trib- utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's.
This volume is based on lectures notes for the courses delivered at the Cimpa Summer School: From Classical to Modern Probability, held at Temuco, Chile, be- th th tween January 8 and 26 , 2001.
Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "e;foundation"e; or support leading by analogy to a knowledge of the latter.
On what grounds can one reasonably expect that a complex financial contract solving a complex real-world issue does not deserve the same thorough scientific treatment as an aeroplane wing or a micro-proces- sor?
During the of Fall 1991, The Centre de Recerca Matematica, a research institute sponsored by the Institut d'Estudis Catalans, devoted a quarter to the study of stochastic analysis.
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.
During the past decade model predictive control (MPC), also referred to as receding horizon control or moving horizon control, has become the preferred control strategy for quite a number of industrial processes.
"e;Stochastic Processes in Quantum Physics"e; addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous.
The seminar on Stochastic Analysis and Mathematical Physics of the Ca- tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro- moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics.
This book contains the proceedings of the conference "e;Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics"e; that was held in the second week of June 2001 at Graz University of Technology, in the capital of Styria, southeastern province of Austria.
Over the last years, stochastic analysis has had an enormous progress with the impetus originating from different branches of mathematics: PDE's and the Malliavin calculus, quantum physics, path space analysis on curved manifolds via probabilistic methods, and more.
These notes had their origin in a postgraduate lecture series I gave at the Eid- genossiche Technische Hochschule (ETH) in Zurich in the Spring of 2000.
This volume contains the Proceedings of the Fourth Seminar on Stochastic Analy- sis, Random Fields and Applications, which took place at the Centro Stefano Fran- scini (Monte Verita) in Ascona (Ticino), Switzerland, from May 20 to 24, 2002.
This textbook gives an introduction to stochastic partial differential equations such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise.
Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles.
Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest.
Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine.
The statistical analysis of extreme data is important for various disciplines, including hydrology, insurance, finance, engineering and environmental sciences.
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts.
This thirteenth volume of the Poincare Seminar Series, Henri Poincare, 1912-2012, is published on the occasion of the centennial of the death of Henri Poincare in 1912.
Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others.
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification.
