Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion | Zendy

Haiyan Yuan | Zendy

Open Access

Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

Author(s) -

Haiyan Yuan

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/1835490

Subject(s) - mathematics , uniqueness , stochastic differential equation , convergence (economics) , brownian motion , euler's formula , numerical stability , mathematical analysis , exponential stability , exponential function , stability (learning theory) , backward euler method , numerical analysis , euler method , euler equations , physics , nonlinear system , computer science , statistics , quantum mechanics , machine learning , economics , economic growth

This paper is concerned with the numerical solutions of semilinear stochastic delay differential equations driven by G-Brownian motion (G-SLSDDEs). The existence and uniqueness of exact solutions of G-SLSDDEs are studied by using some inequalities and the Picard iteration scheme first. Then the numerical approximation of exponential Euler method for G-SLSDDEs is constructed, and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent, and it can reproduce the stability of the analytical solution under some restrictions. Numerical experiments are presented to confirm the theoretical results.

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