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

... 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

... Euler method. In Section , we obtain the convergence of the exponential Euler method to SLSDDEs under Lipschitz condition and the linear growth ...exponential Euler method to ... 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

... To the best knowledge of authors, there is no similar result about almost sure stabil- ity of Runge-Kutta type methods for SDDEs, and nearly all existing results concerned with Euler-Maruyama type schemes. ... See full document

... Euler has general mean-square stability. From Fig. 2, it is easy to confirm general mean- square stability of a numerical solution under the same step-size as Case 1. The results indicate that the split-step ... See full document

... numerical method such as the Euler–Maruyama can match the stability properties of a single linear SDE for sufficiently small ∆ > 0, it is much more demanding to ask a method to maintain ... See full document

... If there is no linear growth condition (4.5) on f , for SDDEs, [35] shows that the backward EM approximations may reproduce the almost sure exponential stability. But for SFDEs, we need to give conditions which can ... See full document

... include, Euler-Maruyama method, Eu- ler-Maruyama method, Runge-Kutta method, Heun method and so ...one-step method of Euler-Maruyama type will be ... See full document

... much stochastic perturbation and history effect this system can tolerate without losing the property of asymptotic ...perturbed equations, let us consider the ... See full document

... the equations to be globally Lipschitz, see [3], [5], for ...the Euler–Maruyama (EM) scheme will converge to the true solutions for a broad class of SDEs without the linear growth condi- tion nor the ... See full document

... Liapunov’s method, Swishchuk and Kazmerchuk [] have presented the stability of a trivial solution of semi-linear stochastic delay differential equations with Markovian switchings and with ... 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

... of Euler-Maruyama (EM) type approximations to the solutions of stochastic differential equations (SDEs) with non-linear and non- Lipschitzian ...a stochastic counterpart of the ... 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

... 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

... 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

... With respect to the aforementioned stochastic systems, the white Gaussian noise is used as the only interference source to depict a random continuous and stable phenomena. In real world applications, however, the ... See full document

... ifications of Theorem 3.1 in [8] such that the modified theorem is able to cover the truncated EM method. Then, we use the modified theorem to prove the convergence and the computational cost of the MLMC ... See full document

... In [23], we established the theory of the strong L q -convergence for 2 ≤ q < p, where p is a parameter in Assumption 2.2. However, the convergence was in the asymptotic form without the convergence rate. Starting ... See full document

... explicit method for nonlinear SDEs. We will call it the truncated EM ...different method referred to as the “Drift- truncated Euler scheme” was introduced in Hutzenthaler & Jentzen ... See full document