Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients

Author(s)
Bibliographic Information

Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients

Martin Hutzenthaler, Arnulf Jentzen

(Memoirs of the American Mathematical Society, no. 1112)

American Mathematical Society, 2015, c2014

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Note

"Volume 236, number 1112 (second of 6 numbers), July 2015"

Includes bibliographical references (p. 95-99)

Description and Table of Contents

Description

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.

Table of Contents

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

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Details
  • NCID
    BB19165801
  • ISBN
    • 9781470409845
  • LCCN
    2015007761
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Providence, R.I.
  • Pages/Volumes
    v, 99 p.
  • Size
    26 cm
  • Parent Bibliography ID
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