On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

Mathematical Problems in Engineering ◽

10.1155/2018/8353065 ◽

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.

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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 ◽

Cited By ~ 1

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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Controllability of a stochastic functional differential equation driven by a fractional Brownian motion

Advances in Difference Equations ◽

10.1186/s13662-018-1565-3 ◽

2018 ◽

Vol 2018 (1) ◽

Cited By ~ 1

Author(s):

Jingqi Han ◽

Litan Yan

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Fractional Brownian Motion ◽

Functional Differential Equation ◽

Stochastic Functional Differential Equation ◽

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 ◽

Cited By ~ 4

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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On the existence and uniqueness of periodic solution for a third-order neutral functional differential equation

International Journal of Mathematical Analysis ◽

10.12988/ijma.2016.6345 ◽

2016 ◽

Vol 10 ◽

pp. 817-831

Author(s):

Samuel A. Iyase ◽

Olawale J. Adeleke

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Functional Differential Equation ◽

Existence And Uniqueness ◽

Neutral Functional Differential Equation ◽

Third Order ◽

Functional Differential

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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 ◽

Cited By ~ 4

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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Stability in Delay Functional Differential Equation established using the BANACH Fixed Point Theorem

International Journal of Advanced Trends in Computer Science and Engineering ◽

10.30534/ijatcse/2019/44862019 ◽

2019 ◽

Vol 8 (6) ◽

pp. 2951-2955

Author(s):

Sizar Abid Mohammed ◽

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Functional Differential Equation ◽

Point Theorem ◽

Banach Fixed Point Theorem ◽

Functional Differential

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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 ◽

Cited By ~ 1

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 ◽

Cited By ~ 13

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 ◽

Cited By ~ 2

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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