scholarly journals Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

2015 ◽  
Vol 125 ◽  
pp. 358-397 ◽  
Author(s):  
Michael Röckner ◽  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Infinite Dimensions ◽  
Uniqueness Of Solutions ◽  
Functional Differential ◽  
Stochastic Functional

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 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.

scholarly journals Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Jianguo Tan ◽  
Hongli Wang ◽  
Yongfeng Guo
Keyword(s):  
Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Poisson Jumps ◽  
Uniqueness Of Solutions ◽  
Linear Growth Condition ◽  
Functional Differential ◽  
Stochastic Functional

A class of neutral stochastic functional differential equations with Poisson jumps (NSFDEwPJs),d[x(t)-G(xt)]=f(xt,t)dt+g(xt,t)dW(t)+h(xt,t)dN(t),t∈[t0,T], with initial valuext0=ξ={ξ(θ):-τ≤θ≤0}, is investigated. First, we consider the existence and uniqueness of solutions to NSFDEwPJs under the uniform Lipschitz condition, the linear growth condition, and the contractive mapping. Then, the uniform Lipschitz condition is replaced by the local Lipschitz condition, and the existence and uniqueness theorem for NSFDEwPJs is also derived.

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