Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Pengju Duan

doi:10.3390/math9090988

Abstract

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

Highlights

Stochastic differential equations driven by G-Brownian motion (G-SDEs) are considered as follows
G-SDEs when an aperiodically intermittent control is added into the drift coefficients
Taking the issue under consideration, we will investigate the stability of (1) with an aperiodically intermittent control added into the drift coefficient dy(t) = f (t, y(t))dt + h(s) g(t, y(t))dh Bi(t) + h(s)σ(t, y(t))dB(t), t ≥ 0, (2)

Summary

Introduction

Stochastic differential equations driven by G-Brownian motion (G-SDEs) are considered as follows. Investigated the stability of a solution of G-SDEs by constructing an aperiodically intermittent control which is set in diffusion coefficient. G-SDEs when an aperiodically intermittent control is added into the drift coefficients. Taking the issue under consideration, we will investigate the stability of (1) with an aperiodically intermittent control added into the drift coefficient dy(t) = f (t, y(t))dt + h(s) g(t, y(t))dh Bi(t) + h(s)σ(t, y(t))dB(t), t ≥ 0,. Differing from Yang et al [13], we investigate the stabilization problem of G-SDEs, whose drift coefficients are added with an aperiodically intermittent control. A new aperiodically intermittent control is designed to stabilize this class stochastic system, driven by G-Brownian motion. An example is presented to show the efficiency of the result

Notations

Main Results

Conclusions