Smoothness and Gaussian Density Estimates for Stochastic Functional Differential Equations with Fractional Noise

In this paper, we study the density of the solution to a class of stochastic functional differential equations driven by fractional Brownian motion. Based on the techniques of Malliavin calculus, we prove the smoothness and establish upper and lower Gaussian estimates for the density.

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Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion

Random Operators and Stochastic Equations ◽

10.1515/rose-2014-0020 ◽

2014 ◽

Vol 22 (4) ◽

Author(s):

Zhi Li ◽

Jiaowan Luo

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Fractional Brownian Motion ◽

Functional Differential Equations ◽

Hurst Parameter ◽

Stochastic Functional Differential Equations ◽

Harnack Inequalities ◽

Functional Differential ◽

Stochastic Functional

AbstractIn this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter

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Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space

Statistics & Probability Letters ◽

10.1016/j.spl.2012.04.013 ◽

2012 ◽

Vol 82 (8) ◽

pp. 1549-1558 ◽

Cited By ~ 98

Author(s):

Brahim Boufoussi ◽

Salah Hajji

Keyword(s):

Hilbert Space ◽

Brownian Motion ◽

Differential Equations ◽

Fractional Brownian Motion ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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Malliavin Calculus for Degenerate Stochastic Functional Differential Equations

Acta Applicandae Mathematicae ◽

10.1007/s10440-007-9121-2 ◽

2007 ◽

Vol 97 (1-3) ◽

pp. 281-295 ◽

Cited By ~ 3

Author(s):

Atsushi Takeuchi

Keyword(s):

Differential Equations ◽

Malliavin Calculus ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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The existence–uniqueness and exponential estimate of solutions for stochastic functional differential equations driven by G‐Brownian motion

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6867 ◽

2020 ◽

Vol 44 (2) ◽

pp. 1639-1650

Author(s):

Faiz Faizullah ◽

Quanxin Zhu ◽

Rahman Ullah

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Functional Differential Equations ◽

Exponential Estimate ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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A Note on the Existence Results for Stochastic Functional Differential Equations Driven by G-Brownian Motion

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2016.5965 ◽

2016 ◽

Vol 13 (11) ◽

pp. 8249-8253

Author(s):

Faiz Faizullah ◽

. Farkhanda ◽

Fawad Hussain

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Functional Differential Equations ◽

Existence Results ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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Viability for stochastic functional differential equations in Hilbert spaces driven by fractional Brownian motion

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.08.016 ◽

2019 ◽

Vol 341 ◽

pp. 93-110

Author(s):

Liping Xu ◽

Jiaowan Luo

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Fractional Brownian Motion ◽

Hilbert Spaces ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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Density Estimates for Solutions of Stochastic Functional Differential Equations

Acta Mathematica Scientia ◽

10.1007/s10473-019-0404-2 ◽

2019 ◽

Vol 39 (4) ◽

pp. 955-970

Author(s):

Nguyen Tien Dung ◽

Ta Cong Son ◽

Tran Manh Cuong ◽

Nguyen Van Tan ◽

Trinh Nhu Quynh

Keyword(s):

Differential Equations ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Density Estimates ◽

Functional Differential ◽

Stochastic Functional

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Exponential stability of neutral stochastic functional differential equations driven by G-Brownian motion

The Journal of Nonlinear Sciences and Applications ◽

10.22436/jnsa.010.04.43 ◽

2017 ◽

Vol 10 (04) ◽

pp. 1830-1841 ◽

Cited By ~ 3

Author(s):

Min Zhu ◽

Junping Li ◽

Yongxiang Zhu

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Exponential Stability ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

Applicable Analysis ◽

10.1080/00036811.2017.1377831 ◽

2017 ◽

Vol 97 (15) ◽

pp. 2555-2572 ◽

Cited By ~ 2

Author(s):

Guangjie Li ◽

Qigui Yang

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Functional Differential Equations ◽

Markovian Switching ◽

Stochastic Functional Differential Equations ◽

Functional Differential ◽

Stochastic Functional

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EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN Lp(Ω, Ch)

Stochastics and Dynamics ◽

10.1142/s0219493709002786 ◽

2009 ◽

Vol 09 (04) ◽

pp. 597-612

Author(s):

HAIBO BAO ◽

DAQING JIANG

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Existence And Uniqueness ◽

Infinite Delay ◽

Functional Differential Equations ◽

Stochastic Functional Differential Equations ◽

Uniqueness Of Solutions ◽

Functional Differential ◽

Stochastic Functional

In this paper, we shall consider the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp(Ω, Ch) space: [Formula: see text] where we assume f : R+ × Lp(Ω, Ch) → Lp(Ω, Rn), g : R+ × Lp(Ω, Ch) → Lp(Ω, L(Rm, Rn)), p > 2, and B(t) is a given m-dimensional Brownian motion.

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