scholarly journals Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3433-3442 ◽  
Author(s):  
Diem Huan ◽  
Ravi Agarwal ◽  
Hongjun Gao

We establish results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert spaces. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Further, the above results are generalized to cover a class of much more general impulsive neutral stochastic delay partial differential equations driven by L?vy noise in infinite dimensions. Finally, an example is provided to illustrate our results.

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yi Shen ◽  
Yan Li

We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.


2020 ◽  
pp. 2150014
Author(s):  
Jiankang Liu ◽  
Wei Xu ◽  
Qin Guo

This paper focuses on systems of stochastic partial differential equations with impulse effects. We establish an averaging principle such that the solution to the complex original nonlinear impulsive stochastic evolution equations can be approximated by that to the more simplified averaged stochastic evolution equations without impulses. By adopting stochastic analysis theory, semigroup approach and inequality technique, sufficient conditions are formulated and the mean square convergence is proved. This ensures that we can concentrate on the averaged system instead of the original system, thus providing a solution for reduction of complexity.


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