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Stochastic Analysis
  • Language: en
  • Pages: 246

Stochastic Analysis

  • Type: Book
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  • Published: 2015
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  • Publisher: Unknown

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Mathematics of the Bond Market
  • Language: en
  • Pages: 401

Mathematics of the Bond Market

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

Stochastic Equations in Infinite Dimensions
  • Language: en
  • Pages: 513

Stochastic Equations in Infinite Dimensions

Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.

Stochastic Partial Differential Equations with Lévy Noise
  • Language: en
  • Pages: 45

Stochastic Partial Differential Equations with Lévy Noise

Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

Stochastic Systems and Optimization
  • Language: en
  • Pages: 388

Stochastic Systems and Optimization

  • Type: Book
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  • Published: 1989-10-27
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  • Publisher: Springer

The meeting intended to continue the traditional line of the foregoing conferences and to focus on topics of present research in the field of stochastic systems and optimization. Particular emphasis was placed on stochastic differential systems both finite and infinite dimensional, filtering, stochastic control, asymptotic methods and periodic systems.

Mathematical Control Theory
  • Language: en
  • Pages: 347

Mathematical Control Theory

This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. This second edition includes new chapte...

Mathematical Control Theory
  • Language: en
  • Pages: 276

Mathematical Control Theory

In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.

Stochastic Processes and Related Topics
  • Language: en
  • Pages: 186

Stochastic Processes and Related Topics

  • Type: Book
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  • Published: 1996-02-09
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  • Publisher: CRC Press

The aim of this volume is to make accessible to a greater audience papers given at the 10th Winterschool on Stochastic Processes in Siegmundsburg, Germany, March 1994. The papers include developments in stochastic analysis, applications to finance mathematics, Markov processes and diffusion processes, stochastic differential equations and stochastic partial differential equations.

Second Order Partial Differential Equations in Hilbert Spaces
  • Language: en
  • Pages: 206

Second Order Partial Differential Equations in Hilbert Spaces

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

Stochastic Partial Differential Equations and Applications - VII
  • Language: en
  • Pages: 360

Stochastic Partial Differential Equations and Applications - VII

  • Type: Book
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  • Published: 2005-10-12
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  • Publisher: CRC Press

Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo