Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients (häftad)
Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
99
Utgivningsdatum
2015-07-30
Förlag
American Mathematical Society
Dimensioner
260 x 180 x 3 mm
Vikt
172 g
ISSN
0065-9266
ISBN
9781470409845
Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients (häftad)

Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

Häftad Engelska, 2015-07-30
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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, 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.
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Övrig information

Martin Hutzenthaler, University of Duisburg-Essen, North Rhine-Westphalia, Germany. Arnulf Jentzen, ETH Zurich, Switzerland.

Innehållsförteckning

Introduction Integrability properties of approximation processes for SDEs Convergence properties of approximation processes for SDEs Examples of SDEs Bibliography