Optimal control of fractional neutral stochastic differential equations with deviated argument governed by Poisson jumps and infinite delay

2019 ◽  
Vol 40 (5) ◽  
pp. 880-899 ◽  
Author(s):  
N. Durga ◽  
P. Muthukumar
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Poisson Jumps ◽  
Deviated Argument

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 The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

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