A New Efficient Explicit Scheme of Order $1.5$ for SDE with Super-linear Drift Coefficient

Abstract

We propose a new explicit numerical scheme for stochastic differential equation with super-linearly growing drift and linearly growing diffusion coefficients which are also twice continuously differentiable. The rate of strong convergence in ${\mathcal{L}}^p$-norm is shown to be equal to $1.5$. Moreover, the scheme is computationally more efficient that the corresponding scheme available in the literature.

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References in corpus (4)

• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• A note on tamed Euler approximations
• Order-preserving strong schemes for SDEs with locally Lipschitz coefficients

Cited by in corpus (2)

• Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
• A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations