Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Lakhel, El Hassan; Tlidi, Abdelmonaim

doi:10.22436/jnsa.011.06.11

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…In [6,18], the authors investigated the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay equations perturbed by FBM with H > 1/2. Controllability of non-autonomous neutral evolution stochastic functional differential equations driven by FBM with H > 1/2 has been proved in [24]. More recently, the global existence, uniqueness and viability results to stochastic functional differential equations in Hilbert spaces driven by FBM when H > 1/2 have been studied in [34].…”

Section: Introductionmentioning

confidence: 99%

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

2021

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In this paper we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion B σ,λ Q (t) with −1/2 < σ < 0 and λ > 0. We first introduce a technical lemma which is crucial in our stability analysis. Then we prove the existence and uniqueness of mild solutions by using semigroup methods. The upper nonlinear noise excitation index of the energy solutions at any finite time t is also obtained. Finally, we consider the exponential asymptotic behavior of mild solutions in mean square.

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Section: Introductionmentioning

confidence: 99%

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

2021

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Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays

Lakhel

Tlidi

2019

Random Operators and Stochastic Equations

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Hermite processes are self-similar processes with stationary increments; the Hermite process of order 1 is fractional Brownian motion (fBm) and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of impulsive neutral stochastic functional differential equations with variable delays driven by Rosenblatt process with index {H\in(\frac{1}{2},1)} , which is a special case of a self-similar process with long-range dependence. More precisely, we prove an existence and uniqueness result, and we establish some conditions, ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

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Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays

Hassan

2019

Proyecciones (Antofagasta)

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Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Cited by 3 publications

References 18 publications

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays

Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays

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