scholarly journals Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Mohamed Rhaima
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
The Stability ◽  
Rassias Stability ◽  
Stochastic Functional

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

scholarly journals General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yue Liu ◽  
Xuejing Meng ◽  
Fuke Wu
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
General Decay ◽  
Stochastic Functional Differential Equations ◽  
General Decay Rate ◽  
Polynomial Coefficients ◽  
Functional Differential ◽  
The Stability ◽  
Stochastic Functional

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. The main aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay stochastic functional differential equations with polynomial coefficients.

scholarly journals Approximations of Numerical Method for Neutral Stochastic Functional Differential Equations with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Differential Equations ◽  
Stochastic Systems ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Em Method ◽  
Functional Differential ◽  
Stochastic Functional

Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama (EM) method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover, we obtain the convergence order of the approximate solutions.

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