A Third Order Weak Approximation Of Multidimensional Ito Stochastic Differential Equations
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Author | : Riu Naito |
Publisher | : |
Total Pages | : |
Release | : 2019 |
Genre | : |
ISBN | : |
Download A Third-Order Weak Approximation of Multidimensional Itô Stochastic Differential Equations Book in PDF, Epub and Kindle
This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler-Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method. The method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions. Numerical examples are shown to confirm the accuracy of the scheme.
Author | : Toshihiro Yamada |
Publisher | : |
Total Pages | : |
Release | : 2019 |
Genre | : |
ISBN | : |
Download A Higher Order Weak Approximation Scheme of Multidimensional Stochastic Differential Equations Using Malliavin Weights Book in PDF, Epub and Kindle
We show a new higher order weak approximation with Malliavin weights for multidimensional stochastic differential equations by extending the method in Takahashi and Yamada (2016). The estimate of global error of the discretization is based on a sharp small time expansion using a Malliavin calculus approach. We give explicit Malliavin weights for second order discretization as polynomials of Brownian motions. The effectiveness is illustrated through an example in option pricing.
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 | : Grigori N. Milstein |
Publisher | : Springer Nature |
Total Pages | : 754 |
Release | : 2021-12-03 |
Genre | : Computers |
ISBN | : 3030820408 |
Download Stochastic Numerics for Mathematical Physics Book in PDF, Epub and Kindle
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 | : Toshihiro Yamada |
Publisher | : |
Total Pages | : |
Release | : 2019 |
Genre | : |
ISBN | : |
Download An Arbitrary High Order Weak Approximation of SDE and Malliavin Monte Carlo Book in PDF, Epub and Kindle
This paper proposes an arbitrary high order weak approximation scheme for multidimensional Stratonovich stochastic differential equations using Malliavin calculus. The scheme efficiently works whether test function is smooth or not. The Malliavin Monte Carlo method, a simple numerical algorithm, is introduced to implement the scheme. Numerical examples illustrate the validity of the method.
Author | : Sabir Umarov |
Publisher | : World Scientific |
Total Pages | : 192 |
Release | : 2018-02-13 |
Genre | : Mathematics |
ISBN | : 9813230991 |
Download Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations Book in PDF, Epub and Kindle
The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.
Author | : Anders Szepessy |
Publisher | : |
Total Pages | : 26 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Adaptive Weak Approximation of Stochastic Differential Equations Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 17 |
Release | : 2000 |
Genre | : |
ISBN | : 9789171706447 |
Download Weak Approximation of Itô Stochastic Differential Equations and Related Adaptive Algorithms Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 110 |
Release | : 2002 |
Genre | : |
ISBN | : |
Download Weak Approximation of Stochastic Differential Equations by Discrete Time Series Book in PDF, Epub and Kindle
Author | : Raúl Tempone Olariaga |
Publisher | : |
Total Pages | : 28 |
Release | : 2002 |
Genre | : |
ISBN | : 9789172833500 |
Download Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations Book in PDF, Epub and Kindle