On Numerical Approximations For Stochastic Differential Equations
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Author | : Peter E. Kloeden |
Publisher | : Springer Science & Business Media |
Total Pages | : 666 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662126168 |
Download Numerical Solution of Stochastic Differential Equations Book in PDF, Epub and Kindle
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 | : Xiling Zhang |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : |
ISBN | : |
Download On Numerical Approximations for Stochastic Differential Equations Book in PDF, Epub and Kindle
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
Download Applied Stochastic Differential Equations Book in PDF, Epub and Kindle
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author | : James Matthew Foster |
Publisher | : |
Total Pages | : |
Release | : 2020 |
Genre | : |
ISBN | : |
Download Numerical Approximations for Stochastic Differential Equations Book in PDF, Epub and Kindle
Author | : Martin Hutzenthaler |
Publisher | : American Mathematical Soc. |
Total Pages | : 112 |
Release | : 2015-06-26 |
Genre | : Mathematics |
ISBN | : 1470409844 |
Download Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients Book in PDF, Epub and Kindle
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.
Author | : Arnulf Jentzen |
Publisher | : SIAM |
Total Pages | : 224 |
Release | : 2011-12-08 |
Genre | : Mathematics |
ISBN | : 1611972000 |
Download Taylor Approximations for Stochastic Partial Differential Equations Book in PDF, Epub and Kindle
This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with H?lder continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right. The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.
Author | : Mohammad Mahbubur Rahman |
Publisher | : |
Total Pages | : 182 |
Release | : 2004 |
Genre | : Stochastic differential equations |
ISBN | : |
Download Numerical Approximations of Stochastic Differential Equations with Applications to Mathematical Neurosciences Book in PDF, Epub and Kindle
Author | : Jialin Hong |
Publisher | : Springer Nature |
Total Pages | : 220 |
Release | : 2019-08-22 |
Genre | : Mathematics |
ISBN | : 9813290692 |
Download Invariant Measures for Stochastic Nonlinear Schrödinger Equations Book in PDF, Epub and Kindle
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Author | : Liying Huang |
Publisher | : |
Total Pages | : 194 |
Release | : 1995 |
Genre | : Stochastic differential equations |
ISBN | : |
Download Stochastic Differential Equations and Their Numerical Approximations Book in PDF, Epub and Kindle
Author | : Rahman, Mohammad Mahbubur |
Publisher | : Ann Arbor, Mich. : University Microfilms International |
Total Pages | : 182 |
Release | : 2004 |
Genre | : Stochastic differential equations |
ISBN | : |
Download Numerical Approximations of Stochastic Differential Equations with Applications to Mathematical Neurosciences [microform] Book in PDF, Epub and Kindle