Author: Erika HausenblasPublisher:
ISBN:
Category :
Languages : en
Pages : 74
Book Description
Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures
Author: Erika HausenblasError Analysis with Applications in Engineering
Author: Zbigniew A. KotulskiPublisher: Springer Science & Business Media
ISBN: 9048135702
Category : Technology & Engineering
Languages : en
Pages : 270
Book Description
Our intention in preparing this book was to present in as simple a manner as possible those branches of error analysis which ?nd direct applications in solving various problems in engineering practice. The main reason for writing this text was the lack of such an approach in existing books dealing with the error calculus. Most of books are devoted to mathematical statistics and to probability theory. The range of applications is usually limited to the problems of general statistics and to the analysis of errors in various measuring techniques. Much less attention is paid in these books to two-dimensional and three-dim- sional distributions, and almost no attention is given to problems connected with the two-dimensional and three-dimensional vectorial functions of independent random variables. The theory of such vectorial functions ?nds new applications connected, for example, with analysis of the positioning accuracy of various mechanisms, among them of robot manipulators and automatically controlled earth-moving and loading machines, such as excavators.
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
Author: Eckhard PlatenPublisher: Springer Science & Business Media
ISBN: 364213694X
Category : Mathematics
Languages : en
Pages : 868
Book Description
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
Applied Stochastic Differential Equations
Author: Simo SärkkäPublisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327
Book Description
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Stochastic Evolution Equations
Author: Wilfried GreckschPublisher: De Gruyter Akademie Forschung
ISBN:
Category : Mathematics
Languages : en
Pages : 188
Book Description
The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Approximations
Author: Mathematical Analysis Of Random Phenomena - Proceedings Of The International Conference
Author: Ana Bela CruzeiroPublisher: World Scientific
ISBN: 9814475696
Category : Mathematics
Languages : en
Pages : 241
Book Description
This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differential equations.While modern stochastic analysis may appear to be an abstract mixture of classical analysis and probability theory, this book shows that, in fact, it can provide versatile tools useful in many areas of applied mathematics where the phenomena being described are random. The geometrical aspects of stochastic analysis, often regarded as the most promising for applications, are specially investigated by various contributors to the volume.
SIAM Journal on Numerical Analysis
Author: Mathematical Analysis of Random Phenomena
Author: Ana Bela CruzeiroPublisher: World Scientific
ISBN: 9812706038
Category : Science
Languages : en
Pages : 241
Book Description
This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differential equations.While modern stochastic analysis may appear to be an abstract mixture of classical analysis and probability theory, this book shows that, in fact, it can provide versatile tools useful in many areas of applied mathematics where the phenomena being described are random. The geometrical aspects of stochastic analysis, often regarded as the most promising for applications, are specially investigated by various contributors to the volume.
Parameter Estimation in Stochastic Differential Equations
Author: Jaya P. N. BishwalPublisher: Springer
ISBN: 3540744487
Category : Mathematics
Languages : en
Pages : 271
Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.