Controllability for Time-dependent Neutral Stochastic Functional Differential Equations with Rosenblatt Process and Impulses

2019 ◽  
Vol 17 (2) ◽  
pp. 286-297 ◽  
Author(s):  
El Hassan Lakhel ◽  
M. A. McKibben
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Time Dependent ◽  
Stochastic Functional Differential Equations ◽  
Rosenblatt Process ◽  
Functional Differential ◽  
Stochastic Functional

Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
El Hassan Lakhel
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Stochastic Functional Differential Equations ◽  
Poisson Jumps ◽  
Neutral Functional Differential Equations ◽  
Rosenblatt Process ◽  
Fixed Point Principle ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this note we consider a class of neutral stochastic functional differential equations with finite delays driven simultaneously by a Rosenblatt process and Poisson process in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point principle. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

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