Almost sure exponential stability of the backward Euler–Maruyama discretization for highly nonlinear stochastic functional differential equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.03.010 ◽

2014 ◽

Vol 236 ◽

pp. 150-160 ◽

Author(s):

Shaobo Zhou ◽

Songfa Xie ◽

Zheng Fang

Keyword(s):

Differential Equation ◽

Exponential Stability ◽

Functional Differential Equation ◽

Stochastic Functional Differential Equation ◽

Almost Sure Exponential Stability ◽

Backward Euler ◽

Highly Nonlinear ◽

Functional Differential ◽

Stochastic Functional

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Almost sure exponential stability of semi-Euler numerical scheme for nonlinear stochastic functional differential equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1809655 ◽

2020 ◽

pp. 1-17

Author(s):

Linna Liu ◽

Feiqi Deng

Keyword(s):

Differential Equation ◽

Exponential Stability ◽

Functional Differential Equation ◽

Numerical Scheme ◽

Stochastic Functional Differential Equation ◽

Almost Sure Exponential Stability ◽

Functional Differential ◽

Stochastic Functional

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Exponential stability of numerical solution to neutral stochastic functional differential equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.05.041 ◽

2015 ◽

Vol 266 ◽

pp. 441-461 ◽

Author(s):

Shaobo Zhou

Keyword(s):

Differential Equation ◽

Exponential Stability ◽

Numerical Solution ◽

Functional Differential Equation ◽

Stochastic Functional Differential Equation ◽

Functional Differential ◽

Stochastic Functional

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Almost sure exponential stability of implicit numerical solution for stochastic functional differential equation with extended polynomial growth condition

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.02.031 ◽

2018 ◽

Vol 330 ◽

pp. 201-212 ◽

Author(s):

Linna Liu ◽

Feiqi Deng ◽

Ting Hou

Keyword(s):

Differential Equation ◽

Exponential Stability ◽

Numerical Solution ◽

Growth Condition ◽

Polynomial Growth ◽

Stochastic Functional Differential Equation ◽

Almost Sure Exponential Stability ◽

Functional Differential ◽

Stochastic Functional ◽

Polynomial Growth Condition

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EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES

Journal of Applied Analysis & Computation ◽

10.11948/20190089 ◽

2020 ◽

Vol 0 (0) ◽

pp. 0-0

Author(s):

Linxin Shu ◽

◽

Xiao-Bao Shu ◽

Quanxin Zhu ◽

Fei Xu ◽

...

Keyword(s):

Differential Equation ◽

Exponential Stability ◽

Functional Differential Equation ◽

Mild Solutions ◽

Second Order ◽

Stochastic Functional Differential Equation ◽

Random Impulses ◽

Functional Differential ◽

Stochastic Functional

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Exponential stability of impulsive neutral stochastic functional differential equation driven by fractional Brownian motion and Poisson point processes

Afrika Matematika ◽

10.1007/s13370-017-0538-0 ◽

2017 ◽

Vol 29 (1-2) ◽

pp. 233-247 ◽

Author(s):

Brahim Boufoussi ◽

Salah Hajji ◽

El Hassan Lakhel

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Exponential Stability ◽

Fractional Brownian Motion ◽

Functional Differential Equation ◽

Point Processes ◽

Poisson Point Processes ◽

Stochastic Functional Differential Equation ◽

Functional Differential ◽

Stochastic Functional

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Stochastic functional differential equation with infinite memory driven by a fractional Brownian motion with Hurst parameter H>1/2

Stochastics ◽

10.1080/17442508.2016.1155589 ◽

2016 ◽

Vol 88 (6) ◽

pp. 884-903 ◽

Author(s):

Don Gayan Wilathgamuwa

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Fractional Brownian Motion ◽

Functional Differential Equation ◽

Hurst Parameter ◽

Stochastic Functional Differential Equation ◽

Infinite Memory ◽

Functional Differential ◽

Stochastic Functional

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

Cybernetics and Systems Analysis ◽

10.1007/s10559-008-9029-5 ◽

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

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Using waveform relaxation methods to approximate neutral stochastic functional differential equation systems

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.04.038 ◽

2015 ◽

Vol 263 ◽

pp. 151-164

Author(s):

Zhencheng Fan

Keyword(s):

Differential Equation ◽

Functional Differential Equation ◽

Waveform Relaxation ◽

Relaxation Methods ◽

Stochastic Functional Differential Equation ◽

Functional Differential ◽

Stochastic Functional

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A note on the neutral stochastic functional differential equation with infinite delay and Poisson jumps in an abstract space

Journal of Mathematical Physics ◽

10.1063/1.3202822 ◽

2009 ◽

Vol 50 (8) ◽

pp. 082704 ◽

Author(s):

Yong Ren ◽

Li Chen

Keyword(s):

Differential Equation ◽

Functional Differential Equation ◽

Infinite Delay ◽

Abstract Space ◽

Poisson Jumps ◽

Stochastic Functional Differential Equation ◽

Functional Differential ◽

Stochastic Functional

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CONJUGATION OF FLOWS FOR STOCHASTIC AND RANDOM FUNCTIONAL DIFFERENTIAL EQUATIONS

Stochastics and Dynamics ◽

10.1142/s021949370100014x ◽

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.

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