Nonparametric estimation of linear multiplier in stochastic differential equations driven by $\alpha$-stable noise

TL;DR

This paper develops a nonparametric method for estimating the linear multiplier in the trend coefficient of stochastic differential equations driven by small $oldsymbol{ extit{ extalpha}}$-stable noise, addressing challenges posed by heavy-tailed noise distributions.

Contribution

It introduces a novel nonparametric estimation technique specifically designed for models with $ extit{ extalpha}$-stable noise, expanding the toolkit for analyzing such stochastic systems.

Findings

Effective estimation of the linear multiplier in $ extit{ extalpha}$-stable driven SDEs

The method performs well with small noise levels

Provides theoretical guarantees for the estimator's consistency

Abstract

We discuss nonparametric estimation of linear multiplier in a trend coefficient in models governed by an $\alpha$-stable small noise.