Statistical inference for discretely sampled stochastic functional differential equations with small noise

Hiroki Nemoto; Yasutaka Shimizu

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arXiv · 2303.10807

Statistical inference for discretely sampled stochastic functional differential equations with small noise

Hiroki Nemoto·Yasutaka Shimizu

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Abstract

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when the dispersion coefficient goes to zero and the sample size goes to infinity, simultaneously.

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Hiroki Nemoto, Yasutaka Shimizu. 2023-03-20. Statistical inference for discretely sampled stochastic functional differential equations with small noise. https://arxiv.org/abs/2303.10807

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