On the existence and uniqueness of $ {\cal Q}^0 $-weak solution to linear conditional mean-field fractional SDE

Kai Xiao; Yonghui Zhou; Kai Xiao; Yonghui Zhou

doi:10.3934/math.2025998

AIMS Mathematics

2025, Volume 10, Issue 9: 22421-22431. doi: 10.3934/math.2025998

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On the existence and uniqueness of $ {\cal Q}^0 $-weak solution to linear conditional mean-field fractional SDE

Kai Xiao ¹,
Yonghui Zhou ^{2
,
,}

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550001, China
2.
School of Big Data and Computer Sciences, Guizhou Normal University, Guiyang 550001, China

Received: 07 July 2025 Revised: 27 August 2025 Accepted: 03 September 2025 Published: 28 September 2025
MSC : Primary 60H10, 91G80; Secondary 60G35, 93E11

With the help of the reference probability measure concept in filtering theory, we proved the existence and uniqueness of the $ {\cal Q}^0 $-weak solution to a linear conditional mean-field fractional SDE with Hurst parameter $ H\in (\frac{1}{2}, 1) $, which will be a foundation of investigating equilibrium of insider trading driven by fractional Brownian motion.
- conditional mean-field fractional SDE,
- $ {\cal Q}^0 $-weak solution,
- filtering theory
Citation: Kai Xiao, Yonghui Zhou. On the existence and uniqueness of $ {\cal Q}^0 $-weak solution to linear conditional mean-field fractional SDE[J]. AIMS Mathematics, 2025, 10(9): 22421-22431. doi: 10.3934/math.2025998

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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 $ {\cal Q}^0 $-weak solution to a linear conditional mean-field fractional SDE with Hurst parameter $ H\in (\frac{1}{2}, 1) $, which will be a foundation of investigating equilibrium of insider trading driven by fractional Brownian motion.

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