Work

Distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Year: 2025

Type: article

Abstract: In this paper, we study a class of distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst $0< H<1/2$ and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the considered equations under some non-Lipschitz conditions by Carathéodory approximation technique. Subsequently, we show that the solutions of distribution dependent stochastic differential equations can be approximated by the solutions of the associated averaged distribution dependent stochastic differential equations in the sense of mean square convergence under certain averaging conditions.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-025-04026-3

Authors: Ziyan Xie, 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: hybrid

Estimated APC paid: $1,890

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