Stochastics

This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes.

This textbook is devoted to the general asymptotic theory of statistical experiments.

This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes.

This book deals with analytic treatments of Markov processes.

This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics.

This book deals with selected problems of machine perception, using various 2D and 3D imaging sensors.

Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space.

This textbook is devoted to the general asymptotic theory of statistical experiments.

Markov processes represent a universal model for a large variety of real life random evolutions.

This textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics.

This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics.

The monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics.

This volume highlights recent advances in data science, including image processing and enhancement on large data, shape analysis and geometry processing in 2D/3D, exploration and understanding of neural networks, and extensions to atypical data types such as social and biological signals.

This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course.

This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis.

Although the study of dynamical systems is mainly concerned with single trans- formations and one-parameter flows (i.

Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations.

In 1931 Erwin Schrodinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times.

The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993.

Disordered systems are statistical mechanics models in random environments.

What is high dimensional probability?

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful.

Discrete stochastics is the theory of discrete probability spaces.

"e;Elegantly written, with obvious appreciation for fine points of higher mathematics.

This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990.

Schrodinger Equations and Diffusion Theory addresses the question "e;What is the Schrodinger equation?

Statistics is strongly tied to applications in different scientific disciplines, and the most challenging statistical problems arise from problems in the sciences.

The proceedings of the summer 1999 Chorin workshop on stochastic climate models captures well the spirit of enthusiasm of the workshop participants engaged in research in this exciting field.

This volume contains a selection of invited papers, presented to the fourth In- Statistical Analysis Based on the L1-Norm and Related ternational Conference on Methods, held in Neuchatel, Switzerland, from August 4-9, 2002.

Commonly there is no natural place in a traditional curriculum for mathematics or statistics, where a bridge between theory and practice fits into.

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.

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.

The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics.

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.

"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 second conference on Fractal Geometry and Stochastics was held at Greifs- wald/Koserow, Germany from August 28 to September 2, 1998.

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior.

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.