[PDF] Top 20 The truncated Euler–Maruyama method for stochastic differential equations

... tic differential equations (SDEs) under the local Lipschitz ...tamed Euler–Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward ... See full document

... EM method was developed in [14] to approximate SDEs with one-sided Lipschitz drift coefficient and the linear growth diffusion ...This method was further developed in [33] while the tamed Milstein ... See full document

... explicit method, called the truncated EM ...the method under some additional ...the truncated EM method would be ...the truncated EM method is more widely ... See full document

... numerical method, then by carefully conducting the numerical sim- ulation one can know whether the SDE is stable or not without using the Lyapunov tech- ... See full document

... The truncated Euler–Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some func- tions of solutions to stochastic ... See full document

... explicit method called the truncated Euler–Maruyama ...new method focuses on those SDEs with both the drift and diffusion coefficients allowed to grow ...the method could be ... See full document

... condition. In 2002, Mao [14] generalized the the well-known Khasminskii test [7] from stochastic differential equations (SDEs) to SDDEs. The Khasminskii-type the- orem established in [14] for SDDEs ... See full document

... At this point, it is worth mentioning how our work compares with that of Higham et al. [18]. Theorem 3.3 in their paper is a very important contribution to the numerical SDE theory. The authors proved strong convergence ... See full document

... of stochastic differential delay equations under the generalized Khasminskii-type conditions, Applied Mathematics and Computation, 217(2011), ...of Euler method for impulsive ... See full document

... for stochastic differential equations (SDEs) has recently received a more and more ...ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize ... See full document

... Let us now return to the SDE (3.1). In Section 3 we have shown that the EM method cannot reproduce the almost sure exponential stability of the SDE. However, our the- ory established in the previous sections shows ... See full document

... exponential Euler method to semi-linear stochastic delay differential equations ...exponential Euler approximation solution converges to the analytic solution with the strong ... See full document

... of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and ...semi-linear stochastic ... See full document

... SSBE method can reproduce the exponential mean-square stability of the exact solution with some restriction on stepsize ∆, but the SIE method can reproduce the exponential mean-square stability ... See full document

... Milstein method and no nonlinear algebra problems are encountered during ...IM method is, to a certain extent, improved even for the non-stiff prob- lem (see Table  in Section ), despite the fact that the ... See full document

... this method in approximating the solution of ...of stochastic Taylor expansions, up to ...the Euler– Maruyama and Milstein schemes had been proposed to apply them in practice or to study their ... See full document

... compensated Euler method shares exponential mean-square stability for any step size t with SDEs with Poisson random measure; that is, the method can preserve exponential mean-square stability without ... See full document

... the stochastic theta method ...the method, the STM is regarded a generalisation of the Euler-Maruyama (EM) method and the backward Euler-Maruyama (BEM) ... See full document

... 12 4 5 6 7 8 9 10 13 14 15 16 17 Convergence analysis of the EM approximate solutions In this section, we will study the convergence of the EM approximate solutions for hybrid SDEs with [r] ... See full document

... neutral stochastic func- tional differential equations (NSFDEs) with jumps is ...the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial ... See full document