Stochastic Space—Time Models and Limit Theorems

Stochastic Space—Time Models and Limit Theorems PDF

Author: L. Arnold

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 270

ISBN-13: 9400953909

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Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad 1n Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialisation and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches wich were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD" , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Limit Theorems for Randomly Stopped Stochastic Processes

Limit Theorems for Randomly Stopped Stochastic Processes PDF

Author: Dmitrii S. Silvestrov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 408

ISBN-13: 0857293907

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This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.

Limit Theorems for Random Fields with Singular Spectrum

Limit Theorems for Random Fields with Singular Spectrum PDF

Author: Nicolai Leonenko

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 410

ISBN-13: 9401146071

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This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.

Probabilistic Methods in Fluids

Probabilistic Methods in Fluids PDF

Author: Ian Malcolm Davies

Publisher: World Scientific

Published: 2003

Total Pages: 383

ISBN-13: 9812703985

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This volume contains recent research papers presented at the international workshop on OC Probabilistic Methods in FluidsOCO held in Swansea. The central problems considered were turbulence and the NavierOCoStokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media."

Probabilistic Methods in Fluids

Probabilistic Methods in Fluids PDF

Author: I M Davies

Publisher: World Scientific

Published: 2003-06-13

Total Pages: 380

ISBN-13: 9814487058

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This volume contains recent research papers presented at the international workshop on “Probabilistic Methods in Fluids” held in Swansea. The central problems considered were turbulence and the Navier–Stokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media. Contents:Probabilistic Approach to Hydrodynamic Equations (S Albeverio & Y Belopolskaya)A Mean Field Result for 3D Vortex Filaments (H Bessaih & F Flandoli)Semilinear Stochastic Wave Equations (P-L Chow)Some Remarks on a Statistical Theory of Turbulent Flows (F Flandoli)On the Dispersion of Sets Under the Action of an Isotropic Brownian Flow (H Lisei & M Scheutzow)A Version of the Law of Large Numbers and Applications (A Shirikyan)A Comparison Theorem for Solutions of Backward Stochastic Differential Equations with Two Reflecting Barriers and Its Applications (T-S Zhang)and other papers Readership: Research mathematicians with an interest in stochastic analysis, turbulence, fluid mechanics and stochastic partial differential equations. Keywords:Stochastic Analysis;Turbulence;Fluid Mechanics

Stochastic Dynamics

Stochastic Dynamics PDF

Author: Hans Crauel

Publisher: Springer Science & Business Media

Published: 2007-12-14

Total Pages: 457

ISBN-13: 0387226559

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Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.

Stochastic Modelling In Biology: Relevant Mathematical Concepts And Recent Applications

Stochastic Modelling In Biology: Relevant Mathematical Concepts And Recent Applications PDF

Author: Tautu Petre

Publisher: #N/A

Published: 1990-12-05

Total Pages: 456

ISBN-13: 9814611921

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These proceedings focus on future prospects as well as on the present status in some important areas of applied probability and mathematical biology. Some papers have educational intentions regarding the mathematical modelling of special biological situations. The workshop was the third one in Heidelberg dealing with stochastic modelling in biology, e.g., cell biology, embryology, oncology, epidemiology and genetics.

Probabilistic Methods in Quantum Field Theory and Quantum Gravity

Probabilistic Methods in Quantum Field Theory and Quantum Gravity PDF

Author: Poul Henrik Damgaard

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 382

ISBN-13: 1461537843

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From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.