Individual-Based Models and Their Limits
Author: Ryszard Rudnicki
Publisher: Springer Nature
Published:
Total Pages: 130
ISBN-13: 3031752708
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Stochastic Dynamics
Author: Hans Crauel
Publisher: Springer Science & Business Media
Published: 2007-12-14
Total Pages: 457
ISBN-13: 0387226559
DOWNLOAD EBOOKFocusing 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.
Effective Dynamics of Stochastic Partial Differential Equations
Author: Jinqiao Duan
Publisher: Elsevier
Published: 2014-03-06
Total Pages: 283
ISBN-13: 0128012692
DOWNLOAD EBOOKEffective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises
Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n
Author: Franco Flandoli
Publisher: CRC Press
Published: 1995-08-03
Total Pages: 94
ISBN-13: 9782884490450
DOWNLOAD EBOOKFirst published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.
An Introduction to Stochastic Filtering Theory
Author: Jie Xiong
Publisher: OUP Oxford
Published: 2008-04-17
Total Pages: 288
ISBN-13: 0191551392
DOWNLOAD EBOOKStochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance. As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.
Transport Barriers and Coherent Structures in Flow Data
Author: George Haller
Publisher: Cambridge University Press
Published: 2023-02-28
Total Pages: 428
ISBN-13: 1009225219
DOWNLOAD EBOOKTransport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. It provides a unified treatment of material developed over the past two decades, focusing on the methods that have a solid foundation and broad applicability to data sets beyond simple model flows. The intended audience ranges from advanced undergraduates to researchers in the areas of turbulence, geophysical flows, aerodynamics, chemical engineering, environmental engineering, flow visualization, computational mathematics and dynamical systems. Detailed open-source implementations of the numerical methods are provided in an accompanying collection of Jupyter notebooks linked from the electronic version of the book.
Three Classes of Nonlinear Stochastic Partial Differential Equations
Author: Jie Xiong
Publisher: World Scientific
Published: 2013
Total Pages: 177
ISBN-13: 981445236X
DOWNLOAD EBOOKThe study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.
Technical Abstract Bulletin
Author:
Publisher:
Published: 1967
Total Pages: 866
ISBN-13:
DOWNLOAD EBOOKChaotic Evolution and Strange Attractors
Author: David Ruelle
Publisher: Cambridge University Press
Published: 1989-09-07
Total Pages: 114
ISBN-13: 9780521368308
DOWNLOAD EBOOKThis book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Modern Methods in Scientific Computing and Applications
Author: Anne Bourlioux
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 503
ISBN-13: 9401005109
DOWNLOAD EBOOKWhen we first heard in the spring of 2000 that the Seminaire de matMmatiques superieures (SMS) was interested in devoting its session of the summer of 200l-its 40th-to scientific computing the idea of taking on the organizational work seemed to us somewhat remote. More immediate things were on our minds: one of us was about to go on leave to the Courant Institute, the other preparing for a research summer in Paris. But the more we learned about the possibilities of such a seminar, the support for the organization and also the great history of the SMS, the more we grew attached to the project. The topics we planned to cover were intended to span a wide range of theoretical and practical tools for solving problems in image processing, thin films, mathematical finance, electrical engineering, moving interfaces, and combustion. These applications alone show how wide the influence of scientific computing has become over the last two decades: almost any area of science and engineering is greatly influenced by simulations, and the SMS workshop in this field came very timely. We decided to organize the workshop in pairs of speakers for each of the eight topics we had chosen, and we invited the leading experts worldwide in these fields. We were very fortunate that every speaker we invited accepted to come, so the program could be realized as planned.
