Work

Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

Year: 2024

Type: article

Abstract: In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10403

Authors: Yongkun Li, Zhicong Bai

Institution: Yunnan University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Award: G4737559954