Results 21 to 30 of about 114,687,083 (175)

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations [PDF]

, 2013
A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs).
Wu, Fuke, Kloeden, Peter E., Mao, Xuerong   +2 more
core   +4 more sources

The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations

Abstract and Applied Analysis, 2012
The numerical approximation of exponential Euler method is constructed for semilinear stochastic differential equations (SDEs). The convergence and mean-square (MS) stability of exponential Euler method are investigated. It is proved that the exponential
Chunmei Shi, Yu Xiao, Chiping Zhang
doaj   +1 more source

Numerical solutions of neutral stochastic functional differential equations [PDF]

, 2008
This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) $d[x(t)-u(x_t)]=f(x_t)dt+g(x_t)dw(t)$, $t\geq 0$.
Wu, Fuke, Mao, Xuerong, Chinese Scholarship Council (Funder)   +2 more
core   +4 more sources

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

Journal of Inequalities and Applications, 2017
The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs).
Ling Zhang
doaj   +1 more source

Mean square exponential stability of numerical methods for stochastic differential delay equations

CoRR, 2023
Mean square exponential stability of $θ$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential stability of the $θ$-EM and MTEM methods for SDDEs, which are different from most existing results under Khasminskii-type
Guangqiang Lan, Qi Liu
openaire   +3 more sources

Nonuniform Mean-square Exponential Dichotomies and Mean-square Exponential Stability

, 2019
In this paper, the existence conditions of nonuniform mean-square exponential dichotomy (NMS-ED) for a linear stochastic differential equation (SDE) are established. The difference of the conditions for the existence of a nonuniform dichotomy between an SDE and an ordinary differential equation (ODE) is that the first one needs an additional assumption,
Zhu, Hailong, Chen, Li, He, Xiuli
openaire   +2 more sources

Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays

Abstract and Applied Analysis, 2013
Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an ...
Shifang Kuang, Yunjian Peng, Feiqi Deng, Wenhua Gao   +3 more
doaj   +1 more source

Stability of numerical method for semi-linear stochastic pantograph differential equations

Journal of Inequalities and Applications, 2016
As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics.
Yu Zhang, Longsuo Li
doaj   +1 more source

On the equivalence of stochastic stability and exponentially stability in l.i.m. for stochastic dynamic system with Markov parameters and switching

Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2017
Sufficient conditions equivalent concepts of stochastic stability and exponential stability in the mean square for stochastic dynamic systems random structure with Markov switching are obtained.
T. O. Лукашів, І. В. Малик
doaj   +1 more source

Square-mean piecewise almost automorphic mild solutions to a class of impulsive stochastic evolution equations

Advances in Difference Equations, 2020
In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions ...
Junwei Liu, Ruihong Ren, Rui Xie
doaj   +1 more source