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Numerical solutions of neutral stochastic functional differential equations [PDF]

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

Stochastic Functional Differential Equations on Manifolds [PDF]

Probability Theory and Related Fields, 2001
In this paper, we study stochastic functional differential equations (sfde\u27s) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde\u27s.
Léandre, Rémi, Mohammed, Salah-Eldin A.   +1 more
core   +5 more sources

Invariant measures for stochastic functional differential equations

Electronic Journal of Probability, 2017
We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and for exponential or subexponential convergence to the equilibrium.
Butkovsky, Oleg, Scheutzow, Michael
core   +3 more sources

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Journal of Applied Mathematics, 2010
Neutral stochastic functional differential equations (NSFDEs) have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition ...
Minggao Xue, Shaobo Zhou, Shigeng Hu
doaj   +3 more sources

Square integrable solutions and stability of a second-order stochastic integro-differential equation [PDF]

Scientific Reports
This article investigates the stochastic asymptotic stability, boundedness, and square integrability of solutions to a class of second-order nonlinear stochastic integro-differential equations with multiple variable delays.
Linda Fatima Oudjedi-Damerdji, Mohammed Meziane, Omar Djidel, Salah Boulaaras, Asma Alharbi   +4 more
doaj   +2 more sources

Newton's method for stochastic functional differential equations

Electronic Journal of Differential Equations, 2012
In this article, we apply Newton's method to stochastic functional differential equations. The first part concerns a first-order convergence. We formulate a Gronwall-type inequality which plays an important role in the proof of the convergence theorem
Monika Wrzosek
doaj   +2 more sources

Stochastic Functional Differential Equation under Regime Switching [PDF]

Discrete Dynamics in Nature and Society, 2012
We discuss stochastic functional differential equation under regime switching dx(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.
Ling Bai, Zhang Kai
openaire   +2 more sources

Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

Journal of Function Spaces, 2021
The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via ...
Abdellatif Ben Makhlouf, Lassaad Mchiri, Mohamed Rhaima   +2 more
doaj   +1 more source

On the Asymptotic Equivalence of Ordinary and Functional Stochastic Differential Equations

Journal of Optimization, Differential Equations and Their Applications, 2023
This paper studies the asymptotic behavior of solutions of linear stochastic functional-differential equations. This behavior is investigated using the method of asymptotic equivalence, according to which an ordinary system of linear differential ...
Olexandr M. Stanzhytskyi, Grygoriy O. Petryna, Maryna V. Hrysenko   +2 more
doaj   +1 more source

Analysis of stochastic neutral fractional functional differential equations

Boundary Value Problems, 2022
This work deals with the large deviation principle which studies the decay of probabilities of certain kind of extremely rare events. We consider stochastic neutral fractional functional differential equation with multiplicative noise and show large ...
Alagesan Siva Ranjani, Murugan Suvinthra, Krishnan Balachandran, Yong-Ki Ma   +3 more
doaj   +1 more source