Existence of the l-th moment of a solution to a stochastic functional-differential equation with the entire prehistory

2008 ◽  
Vol 44 (4) ◽  
pp. 582-590 ◽  
Author(s):  
V. K. Yasinskii ◽  
S. V. Antonyuk
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

CONJUGATION OF FLOWS FOR STOCHASTIC AND RANDOM FUNCTIONAL DIFFERENTIAL EQUATIONS

2001 ◽  
Vol 01 (02) ◽  
pp. 283-298 ◽  
Author(s):  
HANNELORE LISEI
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Random Process ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

The purpose of this paper is to transform a stochastic functional differential equation driven by a continuous helix spatial semimartingale of Kunita type into a random functional differential equation by using a stationary bijective random process.

scholarly journals On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lili Gao ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Brownian Motion ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we consider the random periodic solution to a neutral stochastic functional differential equation driven by Brownian motion. We obtain the existence and uniqueness of the random periodic solution by Banach fixed point theorem. Moreover, we introduce two examples to illustrate our results.

scholarly journals Stochastic Functional Differential Equation under Regime Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Ling Bai ◽  
Zhang Kai
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Regime Switching ◽  
Linear Growth ◽  
Ultimate Boundedness ◽  
Stochastic Functional Differential Equation ◽  
Linear Growth Condition ◽  
Exponentially Stable ◽  
Functional Differential ◽  
Stochastic Functional

We discuss stochastic functional differential equation under regime switchingdx(t)=f(xt,r(t),t)dt+q(r(t))x(t)dW1(t)+σ(r(t))|x(t)|βx(t)dW2(t). We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially stable of this system.

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