Deplay BSDEs driven by fractional Brownian motion

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Sadibou Aidara ◽  
Ibrahima Sane
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Hurst Parameter ◽  
The Past ◽  
Type Integral ◽  
Divergence Type ◽  
Uniqueness Of A Solution

Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.

Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sadibou Aidara ◽  
Yaya Sagna
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Type Integral ◽  
Divergence Type ◽  
Mutually Independent ◽  
Uniqueness Of A Solution

Abstract This paper deals with a class of anticipated backward stochastic differential equations driven by two mutually independent fractional Brownian motions. We essentially establish the existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

Fractional anticipated BSDEs with stochastic Lipschitz coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 143-161
Author(s):  
Ahmadou Bamba Sow ◽  
Bassirou Kor Diouf
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Uniqueness Of A Solution

Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter {H\in(1/2,1)} . We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and prove a comparison theorem in a specific case.

RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

2010 ◽  
Vol 20 (09) ◽  
pp. 2761-2782 ◽  
Author(s):  
M. J. GARRIDO-ATIENZA ◽  
B. MASLOWSKI ◽  
B. SCHMALFUß
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Equations ◽  
Hurst Parameter ◽  
Random Dynamical System ◽  
Random Attractors

In this paper, the asymptotic behavior of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is studied. In particular, it is shown that the corresponding solutions generate a random dynamical system for which the existence and uniqueness of a random attractor is proved.

scholarly journals Anticipated backward doubly stochastic differential equations with non-Liphschitz coefficients

2019 ◽  
Vol 4 (1) ◽  
pp. 101-112 ◽  
Author(s):  
Sadibou Aidara
Keyword(s):  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Fractional Brownian Motions ◽  
Doubly Stochastic ◽  
Type Integral ◽  
Uniqueness Of The Solution ◽  
Divergence Type ◽  
Mutually Independent

AbstractIn this work, we deal with a backward stochastic differential equation driven by two mutually independent fractional Brownian motions (with Hurst parameter greater than 1/2). We establish the existence and uniqueness of the solution in the case of non-Lipschitz condition on the generator. The stochastic integral used throughout the paper is the divergence-type integral.

scholarly journals BSDEs driven by two mutually independent fractional Brownian motions with stochastic Lipschitz coefficients

2019 ◽  
Vol 4 (1) ◽  
pp. 139-150 ◽  
Author(s):  
Sadibou Aidara ◽  
Yaya Sagna
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Backward Stochastic Differential Equation ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Type Integral ◽  
Divergence Type ◽  
Mutually Independent ◽  
Uniqueness Of A Solution

AbstractThis paper deals with a class of backward stochastic differential equation driven by two mutually independent fractional Brownian motions. We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

scholarly journals STOCHASTIC VOLTERRA EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H > 1/2

2012 ◽  
Vol 12 (04) ◽  
pp. 1250004 ◽  
Author(s):  
MIREIA BESALÚ ◽  
CARLES ROVIRA
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Uniqueness Result ◽  
Volterra Equations ◽  
Hurst Parameter ◽  
Stieltjes Integral ◽  
Finite Moments

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.

Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

2019 ◽  
Vol 27 (2) ◽  
pp. 107-122
Author(s):  
Fulbert Kuessi Allognissode ◽  
Mamadou Abdoul Diop ◽  
Khalil Ezzinbi ◽  
Carlos Ogouyandjou
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter

Abstract This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion {S_{Q}^{H}(t)} , with Hurst parameter {H\in(\frac{1}{2},1)} . By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.

A Practical Approach to Fractional Stochastic Dynamics

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Tran Hung Thao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Dynamics ◽  
Stochastic Integral ◽  
Approximation Approach ◽  
Fractional Stochastic Differential Equations ◽  
Definition Of ◽  
Simple Definition

In this note we present some results on stochastic dynamics with respect to a fractional Brownian motion from a L2-approximation approach. A new and simple definition of fractional stochastic integral is introduced and a theorem of existence and uniqueness for fractional stochastic differential equations is established.

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