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Research Article | Open Access

On the existence and uniqueness of Q 0 -weak solution to linear conditional mean-field fractional SDE

Kai Xiao1, Yonghui Zhou2( )
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550001, China
School of Big Data and Computer Sciences, Guizhou Normal University, Guiyang 550001, China
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Abstract

With the help of the reference probability measure concept in filtering theory, we proved the existence and uniqueness of the Q 0 -weak solution to a linear conditional mean-field fractional SDE with Hurst parameter H ∈ ( 1 2 , 1 ), which will be a foundation of investigating equilibrium of insider trading driven by fractional Brownian motion.

Keywords

conditional mean-field fractional SDEQ0-weak solutionfiltering theory
CLC number: Primary 60H10, 91G80; Secondary 60G35, 93E11

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 22421-22431
DOI: 10.3934/math.2025998

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Cite this article:
Xiao K, Zhou Y. On the existence and uniqueness of Q 0 -weak solution to linear conditional mean-field fractional SDE. AIMS Mathematics, 2025, 10(9): 22421-22431. https://doi.org/10.3934/math.2025998

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Received: 07 July 2025
Revised: 27 August 2025
Accepted: 03 September 2025
Published: 28 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)