Work

The Stochastic Linear Theta Method of McKean‐Vlasov Fractional Stochastic Differential Equations Driven by Time‐Changed Brownian Motions

Year: 2026

Type: article

Abstract: ABSTRACT This paper investigates a class of time‐changed McKean–Vlasov fractional stochastic differential equations. The presence of fractional singular kernels invalidates conventional analytical tools, such as the time‐changed Gronwall lemma. To overcome this difficulty, we establish an extended version of the time‐changed Gronwall lemma. Based on this new Gronwall lemma, we prove the existence and uniqueness of strong solutions for the considered equations. Furthermore, strong convergence and convergence rate in finite time of the stochastic linear theta method on the particle system are discussed. Two numerical examples are provided to illustrate the theoretical results.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.71067

Authors: Jun Zhang, Zhi Li, Liping Xu

Institution: Yangtze University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Natural Science Foundation of Hubei Province

OpenAlex ID: W7225467026

FWCI:

Cites: 42

Cited by:

Related to: 10