scholarly journals Some Stochastic Functional Differential Equations with Infinite Delay: A Result on Existence and Uniqueness of Solutions in a Concrete Fading Memory Space

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Hassane Bouzahir ◽  
Brahim Benaid ◽  
Chafai Imzegouan
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Fading Memory ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Memory Space ◽  
Functional Differential ◽  
Stochastic Functional

This paper is devoted to existence and uniqueness of solutions for some stochastic functional differential equations with infinite delay in a fading memory phase space.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN Lp(Ω, Ch)

2009 ◽  
Vol 09 (04) ◽  
pp. 597-612
Author(s):  
HAIBO BAO ◽  
DAQING JIANG
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we shall consider the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp(Ω, Ch) space: [Formula: see text] where we assume f : R+ × Lp(Ω, Ch) → Lp(Ω, Rn), g : R+ × Lp(Ω, Ch) → Lp(Ω, L(Rm, Rn)), p > 2, and B(t) is a given m-dimensional Brownian motion.

scholarly journals Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

2020 ◽  
Vol 8 (5) ◽  
pp. 434-446
Author(s):  
Hussein K. Asker
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Well Posedness ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Exponential Estimates ◽  
Global Condition ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.

Sign in / Sign up

Export Citation Format

Share Document