A note on tamed Euler approximations
作者： Sotirios Sabanis
DOI: 10.1214/ECP.V18-2824
关键词: Stochastic differential equation 、 Mathematical analysis 、 Convergence (routing) 、 Rate of convergence 、 Mathematics 、 Polynomial 、 Diffusion (business) 、 Lipschitz continuity 、 Euler's formula 、 Lipschitz domain
摘要: Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, presented in this article. The diffusion assumed to be continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one-half, for such schemes is recovered when local continuity assumptions replaced by global and, addition, it satisfy polynomial continuity.
harvard.edu
ejpecp.org
ed.ac.uk参考文章(8)
N. V. Krylov, Controlled diffusion processes ,(1980)
Michael B Giles, Lukasz Szpruch, Multilevel Monte Carlo methods for applications in finance arXiv: Computational Finance. ,(2012)
István Gyöngy, A note on Euler's Approximations Potential Analysis. ,vol. 8, pp. 205- 216 ,(1998) , 10.1023/A:1008605221617
Desmond J. Higham, Xuerong Mao, Andrew M. Stuart, Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations SIAM Journal on Numerical Analysis. ,vol. 40, pp. 1041- 1063 ,(2002) , 10.1137/S0036142901389530
Michael B. Giles, Multilevel Monte Carlo Path Simulation Operations Research. ,vol. 56, pp. 607- 617 ,(2008) , 10.1287/OPRE.1070.0496
Martin Hutzenthaler, Arnulf Jentzen, Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients arXiv: Probability. ,(2012)
Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden, Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients Annals of Applied Probability. ,vol. 22, pp. 1611- 1641 ,(2012) , 10.1214/11-AAP803
Martin Hutzenthaler, Peter E. Kloeden, Arnulf Jentzen, Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 467, pp. 1563- 1576 ,(2011) , 10.1098/RSPA.2010.0348