Stability of Hybrid SDEs Driven by fBm

Markovian Switching ◽

Hurst Parameter

In this paper, the exponential stability of stochastic differential equations driven by multiplicative fractional Brownian motion (fBm) with Markovian switching is investigated. The quasi-linear cases with the Hurst parameter H ∈ (1/2, 1) and linear cases with H ∈ (0, 1/2) and H ∈ (1/2, 1) are all studied in this work. An example is presented as a demonstration.

Transportation Inequalities for Neutral Stochastic Differential Equations Driven by Fractional Brownian Motion with Hurst Parameter Lesser Than 1/2

Mediterranean Journal of Mathematics ◽

10.1007/s00009-017-0992-9 ◽

2017 ◽

Vol 14 (5) ◽

Cited By ~ 3

Author(s):

Brahim Boufoussi ◽

Salah Hajji

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Hurst Parameter

Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

Advances in Fuzzy Systems ◽

10.1155/2021/3948493 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Elhoussain Arhrrabi ◽

M’hamed Elomari ◽

Said Melliani ◽

Lalla Saadia Chadli

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Exponential Stability ◽

Fractional Stochastic Differential Equations

Stability Of Solutions ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Existence And Stability ◽

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

EXISTENCE OF STRONG SOLUTIONS AND UNIQUENESS IN LAW FOR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

Stochastics and Dynamics ◽

10.1142/s0219493709002725 ◽

2009 ◽

Vol 09 (03) ◽

pp. 423-435 ◽

Cited By ~ 2

Author(s):

TYRONE DUNCAN ◽

DAVID NUALART

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Strong Solutions ◽

Hurst Parameter ◽

Uniqueness In Law ◽

Pathwise Solutions

In this paper we establish the existence of pathwise solutions and the uniqueness in law for multidimensional stochastic differential equations driven by a multi-dimensional fractional Brownian motion with Hurst parameter H > 1/2.

Semilinear backward doubly stochastic differential equations and SPDEs driven by fractional Brownian motion with Hurst parameter in (0,1/2)

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2011.06.003 ◽

2011 ◽

Vol 135 (8) ◽

pp. 896-935 ◽

Cited By ~ 4

Author(s):

Shuai Jing ◽

Jorge A. León

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Hurst Parameter ◽

Doubly Stochastic

Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter Less than 1/2

Stochastic Analysis and Applications ◽

10.1080/07362990601052052 ◽

2007 ◽

Vol 25 (1) ◽

pp. 105-126 ◽

Cited By ~ 4

Author(s):

Jorge A. León ◽

Jaime San Martín

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Hurst Parameter

On the existence of solutions for stochastic differential equations driven by fractional Brownian motion

Filomat ◽

10.2298/fil1906695l ◽

2019 ◽

Vol 33 (6) ◽

pp. 1695-1700

Author(s):

Zhi Li

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Growth Condition ◽

Linear Growth ◽

Existence Of Solutions ◽

Hurst Parameter ◽

Linear Growth Condition ◽

Discontinuous Drift

In this paper, we are concerned with a class of stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2 < H < 1, and a discontinuous drift. By approximation arguments and a comparison theorem, we prove the existence of solutions to this kind of equations under the linear growth condition.

ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ∈ (⅓, ½)

Stochastics and Dynamics ◽

10.1142/s0219493711003267 ◽

2011 ◽

Vol 11 (02n03) ◽

pp. 243-263 ◽

Cited By ~ 6

Author(s):

MIREIA BESALÚ ◽

DAVID NUALART

Keyword(s):

Dynamical System ◽

Brownian Motion ◽

Continuous Function ◽

Differential Equations ◽

Fractional Calculus ◽

Supremum Norm ◽

Hurst Parameter ◽

Hölder Continuous

In this paper we establish precise estimates for the supremum norm for the solution of a dynamical system driven by a Hölder continuous function of order between ⅓ and ½ using the techniques of fractional calculus. As an application we deduce the existence of moments for the solutions to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(⅓, ½) and we obtain an estimate for the supremum norm of the Malliavin derivative.

An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter

Statistical Inference for Stochastic Processes ◽

10.1007/s11203-020-09214-4 ◽

2020 ◽

Vol 23 (2) ◽

pp. 319-353

Author(s):

Kohei Chiba

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Hurst Parameter ◽

M Estimator

Stochastic Differential Equations driven by Fractional Brownian Motion with Markovian Switching

10.5540/03.2020.007.01.0440 ◽

2020 ◽

Author(s):

Karen Guevara ◽

Marcelo Fragoso

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Markovian Switching

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

Random Operators and Stochastic Equations ◽

10.1515/rose-2021-2058 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

A. Bakka ◽

S. Hajji ◽

D. Kiouach

Keyword(s):

Hilbert Space ◽

Fixed Point ◽

Brownian Motion ◽

Differential Equations ◽

Sufficient Conditions ◽

Integrodifferential Equations ◽

Hurst Parameter ◽

Fixed Point Principle ◽

Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.