Numerical Solution Of Sde Through Computer Experiments
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| Author | : Peter Eris Kloeden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642579132 |
This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations. It also creates an intuitive understanding of the necessary theoretical background. Software containing programs for over 100 problems is available online.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 327 |
| Release | : 2019-05-02 |
| Genre | : Business & Economics |
| ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
| Author | : Peter E. Kloeden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 680 |
| Release | : 2011-06-15 |
| Genre | : Mathematics |
| ISBN | : 9783540540625 |
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
| Author | : Peter E. Kloeden |
| Publisher | : |
| Total Pages | : 292 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : Carlo Laing |
| Publisher | : Oxford University Press |
| Total Pages | : 399 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0199235074 |
Great interest is now being shown in computational and mathematical neuroscience, fuelled in part by the rise in computing power, the ability to record large amounts of neurophysiological data, and advances in stochastic analysis. These techniques are leading to biophysically more realistic models. It has also become clear that both neuroscientists and mathematicians profit from collaborations in this exciting research area.Graduates and researchers in computational neuroscience and stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, will benefit from this comprehensive overview. The series of self-contained chapters, each written by experts in their field, covers key topics such as: Markov chain models for ion channel release; stochastically forced single neurons and populations of neurons; statistical methods for parameterestimation; and the numerical approximation of these stochastic models.Each chapter gives an overview of a particular topic, including its history, important results in the area, and future challenges, and the text comes complete with a jargon-busting index of acronyms to allow readers to familiarize themselves with the language used.
| Author | : Daniel J. Duffy |
| Publisher | : John Wiley & Sons |
| Total Pages | : 551 |
| Release | : 2022-03-14 |
| Genre | : Business & Economics |
| ISBN | : 1119719720 |
This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.
| Author | : Grigori N. Milstein |
| Publisher | : Springer Nature |
| Total Pages | : 754 |
| Release | : 2021-12-03 |
| Genre | : Computers |
| ISBN | : 3030820408 |
This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
| Author | : Uwe Windhorst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1336 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 3642585523 |
An overview of the techniques used in modern neuroscience research with the emphasis on showing how different techniques can optimally be combined in the study of problems that arise at some levels of nervous system organization. This is essentially a working tool for the scientist in the laboratory and clinic, providing detailed step-by-step protocols with tips and recommendations. Most chapters and protocols are organized such that they can be used independently, while cross-references between the chapters, a glossary, a list of suppliers and appendices provide further help.
| Author | : Desmond J. Higham |
| Publisher | : |
| Total Pages | : |
| Release | : 2020-12 |
| Genre | : |
| ISBN | : 9781611976427 |
| Author | : Ivan Dimov |
| Publisher | : Springer |
| Total Pages | : 798 |
| Release | : 2017-04-11 |
| Genre | : Computers |
| ISBN | : 3319570994 |
This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transcendental Equations; Numerical Methods for Differential Equations; High Performance Scientific Computing; and also special topics such as Novel methods in computational finance based on the FP7 Marie Curie Action,Project Multi-ITN STRIKE - Novel Methods in Compu-tational Finance, Grant Agreement Number 304617; Advanced numerical and applied studies of fractional differential equations.
