scholarly journals Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients

2013 ◽  
Vol 238 ◽  
pp. 14-28 ◽  
Author(s):  
Xuerong Mao ◽  
Lukasz Szpruch
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Lipschitz Continuous ◽  
Convergence And Stability

scholarly journals Milstein-type semi-implicit split-step numerical methods for nonlinear stochastic differential equations with locally Lipschitz drift terms

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 1-12 ◽  
Author(s):  
Burhaneddin Izgi ◽  
Coskun Cetin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Solutions ◽  
Rates Of Convergence ◽  
Ginzburg Landau ◽  
Linear Growth Condition ◽  
Locally Lipschitz ◽  
Non Linear ◽  
Ginzburg Landau Equations

We develop Milstein-type versions of semi-implicit split-step methods for numerical solutions of non-linear stochastic differential equations with locally Lipschitz coefficients. Under a one-sided linear growth condition on the drift term, we obtain some moment estimates and discuss convergence properties of these numerical methods. We compare the performance of multiple methods, including the backward Milstein, tamed Milstein, and truncated Milstein procedures on non-linear stochastic differential equations including generalized stochastic Ginzburg-Landau equations. In particular, we discuss their empirical rates of convergence.

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