Hardcover |
* ISBN 978-3-11-025010-7
Series: de Gruyter Studies in Mathematics 38
to be published March 2011
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Offers a first part on basic concepts of probability theory
Then builds on that by conveying material on generators for stable-like processes and Levy processes
A third part offers various applications
Easy to follow presentation
With examples and exercises, so useable as secondary reading for courses
Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space.
This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools.
The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Levy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes.
Tools from Probability and Analysis
Brownian motion
Markov processes and martingales
SDE, ƒÕDE and martingale problems
Processes in Euclidean spaces
Processes in domains with a boundary
Heat kernels for stable-like processes
Continuous-time random walks and fractional dynamics
Complex chains and Feynman integral
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Paperback
* ISBN 978-3-11-025005-3
Series: de Gruyter Textbook
o be published May 2011
The unique, huge and documented collection of online simulations in mathematics and physics
More than 1000 simulations - comfortably usable online
Full package downloadable for home installation
Unrivalled way of learning maths and physics
This is a unique, comprehensive and documented collection of simulations in mathematics and physics: More than 1000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the documentation to the simulations. This is a great way to learn mathematics and physics.
Suitable for courses in Mathetmatics for Engineering and Sciences.
Hardcover
* ISBN 978-3-11-025527-0
Series: de Gruyter Series in Nonlinear Analysis and Applications 15
to be published May 2011
this monograph is devoted to the general problems of global-on-time solvability and blow-up for finite time of initial-value- and initial-boundary-value-problems solutions for nonlinear equations of Sobolev type. It describes the present state of research for existence and nonexistence questions for Cauchy problems and initial-boundary value problems for linear and nonlinear Sobolev type equations. Furthermore a numerical analysis of their solution properties is given, as well as the contemporary state of the mathematical modeling in urgent branches of physics.
Hardcover
ISBN 978-3-11-025026-8
Series: de Gruyter Expositions in Mathematics 55
to be published May 2011
*Global access to PDEs
With detailed proofs
For studends, researcher and a self-study
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces.
The focus on a Hilbert space (rather than an apparently more general Banach space) setting is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential
equations.
In contrast to other texts on partial differential equations which consider either specific types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented.
The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.