Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth

Zhou, Shan; Hu, Chaozhu

doi:10.1007/s10092-016-0173-4

Cited by 11 publications

(3 citation statements)

References 26 publications

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“…[8,9] and the polynomial growth condition (3) in Ref. [17]. The latter is a vital assumption in establishing the strong convergence rate of the implicit EM scheme for highly nonlinear SDEs.…”

Section: Sdes With Polynomial Growing Coefficientsmentioning

confidence: 99%

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Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

MENG,

LYU

2023

Wuhan Univ. J. Nat. Sci.

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In this paper, our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients. When the diffusion coefficient is polynomially growing or linearly growing, the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval [0,T], respectively. In both situations, the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required. Two examples are provided to illustrate the theory.

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Section: Sdes With Polynomial Growing Coefficientsmentioning

confidence: 99%

“…( 4) under Assumptions 1 and 2 with α ≥ 2α i and a > ∑ i = 1 n a i (see Ref. [17]). Let R > 0 be an arbitrary number and x(t) be the solution of Eq.…”

Section: Sdes With Polynomial Growing Coefficientsmentioning

confidence: 99%

Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

MENG,

LYU

2023

Wuhan Univ. J. Nat. Sci.

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“…Secondly, the requirement on the step size of the method is significantly released compared with the existing works, which is a stand-alone interesting result. It should be mentioned that many other interesting numerical methods have been proposed for SDDEs, for example [1,2,3,4,8,9,11,10,17,18,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods

Bao

Tang

Shen

et al. 2019

Preprint

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In this paper, a general theorem on the equivalence of pth moment stability between stochastic differential delay equations (SDDEs) and their numerical methods is proved under the assumptions that the numerical methods are strongly convergent and have the bouneded pth moment in the finite time. The truncated Euler-Maruyama (EM) method is studied as an example to illustrate that the theorem indeed covers a large ranges of SDDEs. Alongside the investigation of the truncated EM method, the requirements on the step size of the method are significantly released compared with the work, where the method was initially proposed.

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Computing a Quantity of Interest from Observational Data

et al. 2018

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Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth

Cited by 11 publications

References 26 publications

Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations

Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods

Computing a Quantity of Interest from Observational Data

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