论文信息 - A novel approach to construct numerical methods for stochastic differential equations - 字舞流文

A novel approach to construct numerical methods for stochastic differential equations

In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.

Nikolaos Halidias | N. Halidias

[1] Andrew M. Stuart,et al. Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations , 2002, SIAM J. Numer. Anal..

[2] Nikolaos Halidias. Semi-discrete approximations for stochastic differential equations and applications , 2012, Int. J. Comput. Math..

[3] P. Kloeden,et al. Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4] Xuerong Mao,et al. Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients , 2012, J. Comput. Appl. Math..

[5] T. Faniran. Numerical Solution of Stochastic Differential Equations , 2015 .

[6] Andreas Neuenkirch,et al. CONVERGENCE OF NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN MATHEMATICAL FINANCE , 2012, 1204.6620.

[7] Xuerong Mao,et al. Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients , 2013 .

[8] P. Kloeden,et al. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients , 2010, 1010.3756.