Approximate controllability of second-order neutral stochastic differential equations with infinite delay and Poisson jumps

2015 ◽  
Vol 28 (5) ◽  
pp. 1033-1048 ◽  
Author(s):  
Muthukumar Palanisamy ◽  
Rajivganthi Chinnathambi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Second Order ◽  
Poisson Jumps

scholarly journals Well posedness results for higher-order neutral stochastic differential equations driven by Poisson jumps and Rosenblatt process

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 353-365
Author(s):  
K. Ramkumar ◽  
K. Ravikumar ◽  
A. Anguraj ◽  
Hamdy Ahmed
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Successive Approximation Method ◽  
Poisson Jumps ◽  
Rosenblatt Process

In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of higher-order nonautonomous neutral stochastic differential equations (NSDEs) with infinite delay driven by Poisson jumps and Rosenblatt process in Hilbert space. More precisely, using semigroup theory and successive approximation method, we establish a set of sufficient conditions for obtained the required result. Further, the result is deduced to study the higher-order autonomous system. Finally, examples are provided to demonstrate the obtain results.

scholarly journals Exponential stability for neutral stochastic partial integro-differential equations of second order with poisson jumps

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5173-5190
Author(s):  
Alka Chadha
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Mild Solution ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Second Order ◽  
Poisson Jumps ◽  
Fixed Point Principle ◽  
Poisson Jump

This paper studies the existence, uniqueness and the exponential stability in p-th moment of the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. The existence and uniqueness of the mild solution of neutral second order stochastic differential equation is first established by means of Banach fixed point principle and stochastic analysis. The exponential stability in the p-th moment for the mild solution to impulsive neutral stochastic integrodifferential equations with Poisson jump is obtained by establishing an integral inequality.

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