Stability of Neutral Stochastic Delay Differential Equation

2012 ◽  
Vol 192 ◽  
pp. 346-350
Author(s):  
Rong Hu ◽  
De Jun Shao

The paper discusses the pth moment stability of neutral stochastic differential equation with multiple variable delays. The stability is more general and representative than the exponential stability. This investigation uses a specific Lyapunov function based on usual methods. And it discusses the neutral stochastic differential equations with multiple variable delays which is much more general form. Finally a two dimensional half-linear example is discussed to illustrate the theory.

2015 ◽  
Vol 15 (03) ◽  
pp. 1550018 ◽  
Author(s):  
Luu Hoang Duc ◽  
Björn Schmalfuß ◽  
Stefan Siegmund

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a Hölder space which is separable.


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