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Convergence rates of theta-method for NSDDEs under non-globally Lipschitz continuous coefficients. (English) Zbl 07365323

Summary: This paper is concerned with strong convergence and almost sure convergence for neutral stochastic differential delay equations under non-globally Lipschitz continuous coefficients. Convergence rates of \(\theta \)-EM schemes are given for these equations driven by Brownian motion and pure jumps, respectively, where the drift terms satisfy locally one-sided Lipschitz conditions, and diffusion coefficients obey locally Lipschitz conditions, and the corresponding coefficients are highly nonlinear with respect to the delay terms.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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