Upper Error Bounds for Approximations of Stochastic Differential Equations with Markovian Switching PDF Download
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Languages : en
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Author: Erich Novak
Publisher: Springer
ISBN: 3540459871
Category : Mathematics
Languages : en
Pages : 118
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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).
Author: Saadia Ghazali
Publisher:
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Category :
Languages : en
Pages :
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Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327
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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author: Erika Hausenblas
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
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Author: Terry Lynch
Publisher: LAP Lambert Academic Publishing
ISBN: 9783843359351
Category : Markov processes
Languages : en
Pages : 240
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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.
Author: Jesse David Mason
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 272
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Author: Martin Hutzenthaler
Publisher:
ISBN: 9781470422783
Category : Differential operators
Languages : en
Pages : 99
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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, we 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, we illustrate our results for several SDEs from finance, physics, biology and chemistry.
Author: Svetlana Janković
Publisher:
ISBN: 9788683481507
Category : Stochastic difference equations
Languages : en
Pages : 254
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Author: Chenggui Yuan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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