Multilayer heat equations and their solutions via oscillating integral transforms

Itkin, Andrey; Lipton, Alexander; Muravey, Dmitry

doi:10.1016/j.physa.2022.127544

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…Beyond theoretical studies, simulation and inference are also necessary tools for practical purposes. For some example of applications in various fields (see e.g., Bounebache & Zambotti, 2014; Cantrell & Cosner, 1999; Decamps et al, 2006; Gairat & Shcherbakov, 2017; Itkin et al, 2022; Mota & Esquível, 2014; Ovaskainen & Cornell, 2003; Ramirez et al, 2006; Zhang, 2000 among others).…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood estimator for skew Brownian motion: The convergence rate

Lejay,

Mazzonetto

2023

Scandinavian J Statistics

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We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence of estimators for the SBM, we prove a conjecture left open that the MLE has asymptotically a mixed normal distribution involving the local time with a rate of convergence of order 1/4. We also give a series expansion of the MLE and study the asymptotic behavior of the score and its derivatives, as well as their variation with the skewness parameter. In particular, we exhibit a specific behavior when the SBM is actually a Brownian motion, and quantify the explosion of the coefficients of the expansion when the skewness parameter is close to −1 or 1.This article is protected by copyright. All rights reserved.

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