Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Upper Error Bounds for Approximations of Stochastic Differential Equations with Markovian Switching
Author: Deterministic and Stochastic Error Bounds in Numerical Analysis
Author: Erich NovakPublisher: Springer
ISBN: 3540459871
Category : Mathematics
Languages : en
Pages : 118
Book Description
In these notes different deterministic and stochastic error bounds of numerical analysis are investigated. For many computational problems we have only partial information (such as n function values) and consequently they can only be solved with uncertainty in the answer. Optimal methods and optimal error bounds are sought if only the type of information is indicated. First, worst case error bounds and their relation to the theory of n-widths are considered; special problems such approximation, optimization, and integration for different function classes are studied and adaptive and nonadaptive methods are compared. Deterministic (worst case) error bounds are often unrealistic and should be complemented by different average error bounds. The error of Monte Carlo methods and the average error of deterministic methods are discussed as are the conceptual difficulties of different average errors. An appendix deals with the existence and uniqueness of optimal methods. This book is an introduction to the area and also a research monograph containing new results. It is addressd to a general mathematical audience as well as specialists in the areas of numerical analysis and approximation theory (especially optimal recovery and information-based complexity).
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.
Analytic Approximations of Solutions to Stochastic Differential Equations
Author: Svetlana JankovićPublisher:
ISBN: 9788683481507
Category : Stochastic difference equations
Languages : en
Pages : 254
Book Description
Large Fluctuations of Stochastic Differential Equations
Author: Terry LynchPublisher: LAP Lambert Academic Publishing
ISBN: 9783843359351
Category : Markov processes
Languages : en
Pages : 240
Book Description
This monograph deals with the asymptotic behaviour, and in particular the largest fluctuations, of various classes of stochastic differential equations (SDEs) and their discretisations. Equations subject to Markovian switching are also studied, allowing the drift and diffusion coefficients to switch randomly according to a Markov jump process. The assumptions are motivated by the large fluctuations experienced by financial markets which are subjected to random regime shifts. Such results are then applied to a variant of the classical Geometric Brownian Motion (GBM) market model. Moreover it is shown that discrete approximations to these equations, using standard and split-step implicit Euler-Maruyama methods, exhibit asymptotic behaviour which is consistent with their continuous-time counterparts.
Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures
Author: Erika HausenblasProceedings of the Conference on Stochastic Differential Equations and Applications
Author: Jesse David MasonPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 272
Book Description
Numerical Solutions and Stability of Stochastic Differential Equations with Markovian Switching
Author: Chenggui YuanApproximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions
Author: Krystyna TwardowskaPublisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 64
Book Description