Work

Asymptotic Analysis of a Kernel-Type Estimator for Parabolic Stochastic Partial Differential Equations Driven by Cylindrical Sub-Fractional Brownian Motion

Year: 2025

Type: article

Abstract: The main purpose of the present paper is to investigate the problem of estimating the time-varying coefficient in a stochastic parabolic equation driven by a sub-fractional Brownian motion. More precisely, we introduce a kernel-type estimator for the time-varying coefficient θ(t) in the following evolution equation:du(t,x)=(A0+θ(t)A1)u(t,x)dt+dξH(t,x),x∈[0,1],t∈(0,T],u(0,x)=u0(x), where ξH(t,x) is a cylindrical sub-fractional Brownian motion in L2[0,T]×[0,1], and A0+θ(t)A1 is a strongly elliptic differential operator. We obtain the asymptotic mean square error and the limiting distribution of the proposed estimator. These results are proved under some standard conditions on the kernel and some mild conditions on the model. Finally, we give an application for the confidence interval construction.

Source: Mathematics

DOI: 10.3390/math13162627

Authors: Abdelmalik Keddi, Salim Bouzebda, Fethi Madani

Institutions: University of Tamanghasset, Université de Technologie de Compiègne, Laboratoire de mathématiques appliquées de Compiègne, Université de Saida Dr Moulay Tahar

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4413348401

FWCI:

Cites: 49

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Related to: 10