On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients

Chaman Kumar; Sotirios Sabanis

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arXiv · 1601.02695

On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients

Chaman Kumar·Sotirios Sabanis

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Abstract

A new class of explicit Milstein schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these explicit schemes converge in $\mathcal L^p$ to the solution of the corresponding SDEs with optimal rate.

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BibTeX RIS

Chaman Kumar, Sotirios Sabanis. 2016-01-11. On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients. https://arxiv.org/abs/1601.02695

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