Author: Saadia GhazaliPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The global error in weak approximations of stochastic differential equations
Author: Saadia GhazaliApplied 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.
Adaptive Weak Approximation of Stochastic Differential Equations
Author: Anders SzepessyWeak Approximation of Stochastic Differential Equations by Discrete Time Series
Author: Stochastic Calculus of Variations in Mathematical Finance
Author: Paul MalliavinPublisher: Springer Science & Business Media
ISBN: 3540307990
Category : Business & Economics
Languages : en
Pages : 148
Book Description
Highly esteemed author Topics covered are relevant and timely
On the Global Error of Itô-Taylor Schemes for Strong Approximation of Scalar Stochastic Differential Equations
Author: Norbert HofmannA Higher Order Weak Approximation Scheme of Multidimensional Stochastic Differential Equations Using Malliavin Weights
Author: Toshihiro YamadaPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
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.
Numerical Solution of Stochastic Differential Equations
Author: Peter E. KloedenPublisher: Springer Science & Business Media
ISBN: 3662126168
Category : Mathematics
Languages : en
Pages : 666
Book Description
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
Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations
Author: Raúl Tempone OlariagaPublisher:
ISBN: 9789172833500
Category :
Languages : en
Pages : 28
Book Description
Stochastic Numerics for Mathematical Physics
Author: Grigori N. MilsteinPublisher: Springer Nature
ISBN: 3030820408
Category : Computers
Languages : en
Pages : 754
Book Description
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.