Nonparametric estimation for stochastic differential equations driven by mixed fractional Brownian motion with random effects
type: Item
instance of: scholarly article
title: Nonparametric estimation for stochastic differential equations driven by mixed fractional Brownian motion with random effects
zbMATH Open document ID: 1479.62067
published in: Sankhyā. Series A
publication date: 2021-09-01T00:00:00Z
review text: The paper under review deals with the problem of nonparametric estimation of the density of random effects in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion. The author starts with an overview of some properties of stochastic processes, which are solutions of stochastic differential equations driven by a mixed fractional Brownian motion. Next, he proceeds with introducing a computable estimator of the unknown random effects' density function and proves its consistency in a way analogous to [\textit{M. El Omari} et al., Statistics 53, No. 4, 753--769 (2019; Zbl 1440.62318)], thus indicating that similar results continue to hold for processes driven by a mixed fractional Brownian motion. Finally, the asymptotic distribution of the proposed estimator is derived.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60G22
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 7389299
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: random effects
zbMATH Keywords: nonparametric estimation
zbMATH Keywords: kernel method
zbMATH Keywords: mixed fractional Brownian motion
author: B. L. S. Prakasa Rao
reviewed by: Joseph Melamed
MaRDI profile type: Publication
full work available at URL: s13171-020-00230-3
OpenAlex ID: W3110119765
Wikidata QID: Q115376143
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DOI: 10.1007/S13171-020-00230-3
description: scientific article; zbMATH DE number 7389299