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Hypercontractivity for functional stochastic differential equations [PDF]
Stochastic Processes and their Applications, 2015 An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique invariant probability measure $ $ in entropy, $L^2( )$ and the totally variational norm, and it is compact in $L^2(
Applebaum +27 more
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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) +2 more
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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 +1 more
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Linear stochastic differential equations with functional boundary conditions [PDF]
The Annals of Probability, 2002 We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional independence ...
Alabert, Aureli, Ferrante, Marco
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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
Functional Solutions of Stochastic Differential Equations
MathematicsWe present an integration condition ensuring that a stochastic differential equation dXt=μ(t,Xt)dt+σ(t,Xt)dBt, where μ and σ are sufficiently regular, has a solution of the form Xt=Z(t,Bt).
Imme van den Berg
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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
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Square integrable solutions and stability of a second-order stochastic integro-differential equation [PDF]
Scientific ReportsThis 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 +4 more
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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
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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 +2 more
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