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

Released on by Martin Hutzenthaler
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  • Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients Book Detail

  • Author : Martin Hutzenthaler
  • Release Date : 2015
  • Publisher :
  • Genre : Differential operators
  • Pages : 99
  • ISBN 13 : 9781470422783
  • File Size : 31,31 MB
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Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients by Martin Hutzenthaler PDF Summary

Book 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, 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.

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