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

Hiroki Nemoto () and Yasutaka Shimizu ()
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Hiroki Nemoto: Waseda University
Yasutaka Shimizu: Waseda University

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 2, No 7, 427-456

Abstract: 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 a small dispersion coefficient $$\varepsilon \rightarrow 0$$ ε → 0 and sample size $$n\rightarrow \infty $$ n → ∞ simultaneously.

Keywords: Stochastic delay equation; Functional delay; Discrete observations; Minimum contrast estimator; Small noise; Asymptotic normality; Primary 62M20; Secondary 62F12; 62E20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-023-09299-7

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