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Time Discretization Solution Of Stochastic Differential Equations


Time Discretization Solution Of Stochastic Differential Equations
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Time Discretization Solution Of Stochastic Differential Equations


Time Discretization Solution Of Stochastic Differential Equations
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Author : Nicholas Yannios
language : en
Publisher:
Release Date : 1995

Time Discretization Solution Of Stochastic Differential Equations written by Nicholas Yannios and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Stochastic differential equations categories.




Numerical Solution Of Stochastic Differential Equations


Numerical Solution Of Stochastic Differential Equations
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Author : Peter E. Kloeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Numerical Solution Of Stochastic Differential Equations written by Peter E. Kloeden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.


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



Continuous Time Random Walks For The Numerical Solution Of Stochastic Differential Equations


Continuous Time Random Walks For The Numerical Solution Of Stochastic Differential Equations
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Author : Nawaf Bou-Rabee
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08

Continuous Time Random Walks For The Numerical Solution Of Stochastic Differential Equations written by Nawaf Bou-Rabee and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Random walks (Mathematics) categories.


This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.



Numerical Solution Of Stochastic Differential Equations With Jumps In Finance


Numerical Solution Of Stochastic Differential Equations With Jumps In Finance
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Author : Eckhard Platen
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23

Numerical Solution Of Stochastic Differential Equations With Jumps In Finance written by Eckhard Platen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.


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


Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02

Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.


With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.



Numerical Solution Of Sde Through Computer Experiments


Numerical Solution Of Sde Through Computer Experiments
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Author : Peter Eris Kloeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Solution Of Sde Through Computer Experiments written by Peter Eris Kloeden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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.



Approximating Solutions Of Backward Doubly Stochastic Differential Equations With Measurable Coefficients Using A Time Discretization Scheme


Approximating Solutions Of Backward Doubly Stochastic Differential Equations With Measurable Coefficients Using A Time Discretization Scheme
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Author : Cyrus Yeadon
language : en
Publisher:
Release Date : 2015

Approximating Solutions Of Backward Doubly Stochastic Differential Equations With Measurable Coefficients Using A Time Discretization Scheme written by Cyrus Yeadon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.




Stochastic Differential Equations And Applications


Stochastic Differential Equations And Applications
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Author : Avner Friedman
language : en
Publisher: Academic Press
Release Date : 2014-06-20

Stochastic Differential Equations And Applications written by Avner Friedman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.


Stochastic Differential Equations and Applications, Volume 2 is an eight-chapter text that focuses on the practical aspects of stochastic differential equations. This volume begins with a presentation of the auxiliary results in partial differential equations that are needed in the sequel. The succeeding chapters describe the behavior of the sample paths of solutions of stochastic differential equations. These topics are followed by a consideration of an issue whether the paths can hit a given set with positive probability, as well as the stability of paths about a given manifold and with spiraling of paths about this manifold. Other chapters deal with the applications to partial equations, specifically with the Dirichlet problem for degenerate elliptic equations. These chapters also explore the questions of singular perturbations and the existence of fundamental solutions for degenerate parabolic equations. The final chapters discuss stopping time problems, stochastic games, and stochastic differential games. This book is intended primarily to undergraduate and graduate mathematics students.



Numerical Approximation Of Ordinary Differential Problems


Numerical Approximation Of Ordinary Differential Problems
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Author : Raffaele D'Ambrosio
language : en
Publisher: Springer Nature
Release Date : 2023-09-26

Numerical Approximation Of Ordinary Differential Problems written by Raffaele D'Ambrosio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-26 with Mathematics categories.


This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs. The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and rather self-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs. The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.



A Brief Analysis Of Certain Numerical Methods Used To Solve Stochastic Differential Equations


A Brief Analysis Of Certain Numerical Methods Used To Solve Stochastic Differential Equations
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Author : Nadrajh Govender
language : en
Publisher:
Release Date : 2006

A Brief Analysis Of Certain Numerical Methods Used To Solve Stochastic Differential Equations written by Nadrajh Govender and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematical models categories.