Zdzislaw Brzezniak's Books

Basic Stochastic Processes

A Course Through Exercises

By: Zdzislaw Brzezniak,Tomasz Zastawniak

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Basic Stochastic Processes

A Course Through Exercises

By: Zdzislaw Brzezniak,Tomasz Zastawniak

Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

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244

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447105338

ISBN 13

9781447105336

Stochastic Ferromagnetism

Analysis and Numerics

By: Lubomir Banas,Zdzislaw Brzezniak,Mikhail Neklyudov,Andreas Prohl

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Stochastic Ferromagnetism

Analysis and Numerics

By: Lubomir Banas,Zdzislaw Brzezniak,Mikhail Neklyudov,Andreas Prohl

This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.

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Page Count

248

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110307103

ISBN 13

9783110307108

Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

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Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

This volume deals with the analysis of nonlinear evolution problems described by partial differential equations having random or stochastic parameters. The emphasis throughout is on the actual determination of solutions, rather than on proving the existence of solutions, although mathematical proofs are given when this is necessary from an applications point of view. The content is divided into six chapters. Chapter 1 gives a general presentation of mathematical models in continuum mechanics and a description of the way in which problems are formulated. Chapter 2 deals with the problem of the evolution of an unconstrained system having random space-dependent initial conditions, but which is governed by a deterministic evolution equation. Chapter 3 deals with the initial-boundary value problem for equations with random initial and boundary conditions as well as with random parameters where the randomness is modelled by stochastic separable processes. Chapter 4 is devoted to the initial-boundary value problem for models with additional noise, which obey Ito-type partial differential equations. Chapter 5 is essential devoted to the qualitative and quantitative analysis of the chaotic behaviour of systems in continuum physics. Chapter 6 provides indications on the solution of ill-posed and inverse problems of stochastic type and suggests guidelines for future research. The volume concludes with an Appendix which gives a brief presentation of the theory of stochastic processes. Examples, applications and case studies are given throughout the book and range from those involving simple stochasticity to stochastic illposed problems. For applied mathematicians, engineers and physicists whose work involves solving stochastic problems.

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Page Count

228

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401118205

ISBN 13

9789401118200

Basic Stochastic Processes

A Course Through Exercises

By: Zdzislaw Brzezniak,Tomasz Zastawniak

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Basic Stochastic Processes

A Course Through Exercises

By: Zdzislaw Brzezniak,Tomasz Zastawniak

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Page Count

244

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447105338

ISBN 13

9781447105336

Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

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Nonlinear Stochastic Evolution Problems in Applied Sciences

By: N. Bellomo,Zdzislaw Brzezniak,L.M. de Socio

One service mathematics has rendered the 'Et moi, ...• si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aIle.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; thererore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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Page Count

219

Publisher

Springer

Published Date

ISBN 10

9401048037

ISBN 13

9789401048033

Book's by Zdzislaw Brzezniak

Basic Stochastic Processes

Basic Stochastic Processes

Stochastic Ferromagnetism

Stochastic Ferromagnetism

Nonlinear Stochastic Evolution Problems in Applied Sciences

Nonlinear Stochastic Evolution Problems in Applied Sciences

Basic Stochastic Processes

Basic Stochastic Processes

Nonlinear Stochastic Evolution Problems in Applied Sciences

Nonlinear Stochastic Evolution Problems in Applied Sciences

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