scholarly journals A fractional Brownian field indexed byL2and a varying Hurst parameter

2015 ◽  
Vol 125 (4) ◽  
pp. 1394-1425 ◽  
Author(s):  
Alexandre Richard
Keyword(s):  
Hurst Parameter ◽  
Fractional Brownian Field

A FRACTIONAL POISSON EQUATION: EXISTENCE, REGULARITY AND APPROXIMATIONS OF THE SOLUTION

2009 ◽  
Vol 09 (04) ◽  
pp. 519-548 ◽  
Author(s):  
MARTA SANZ-SOLÉ ◽  
IVÁN TORRECILLA
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Existence And Uniqueness ◽  
Hurst Parameter ◽  
Stochastic Convolution ◽  
Green Kernel ◽  
Sample Paths ◽  
Fractional Brownian Field ◽  
Monotonicity Methods ◽  
Stochastic Boundary

We consider a stochastic boundary value elliptic problem on a bounded domain D ⊂ ℝk, driven by a fractional Brownian field with Hurst parameter H = (H1,…,Hk) ∈ [½, 1[k. First, we define the stochastic convolution derived from the Green kernel and prove some properties. Using monotonicity methods, we prove the existence and uniqueness of solution along with regularity of the sample paths. Finally, we propose a sequence of lattice approximations and prove its convergence to the solution of the SPDE at a given rate.

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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
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.

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

scholarly journals Solving Arbitrage Problem on the Financial Market Under the Mixed Fractional Brownian Motion With Hurst Parameter H ∈]1/2,3/4[

2019 ◽  
Vol 11 (1) ◽  
pp. 76
Author(s):  
Eric Djeutcha ◽  
Didier Alain Njamen Njomen ◽  
Louis-Aimé Fono
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Market ◽  
Existence And Uniqueness ◽  
Hurst Parameter ◽  
Existence And Uniqueness Theorem ◽  
Martingale Approximation ◽  
Arbitrage Opportunities ◽  
Mixed Fractional Brownian Motion ◽  
Geometric Fractional Brownian Motion

This study deals with the arbitrage problem on the financial market when the underlying asset follows a mixed fractional Brownian motion. We prove the existence and uniqueness theorem for the mixed geometric fractional Brownian motion equation. The semi-martingale approximation approach to mixed fractional Brownian motion is used to eliminate the arbitrage opportunities.

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

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

scholarly journals ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL

2018 ◽  
Vol 35 (1) ◽  
pp. 198-231 ◽  
Author(s):  
Weilin Xiao ◽  
Jun Yu
Keyword(s):  
Strong Consistency ◽  
Asymptotic Theory ◽  
Least Squares Method ◽  
Estimation Method ◽  
Hurst Parameter ◽  
Stationary Case ◽  
Vasicek Model ◽  
Continuous Record ◽  
Recurrent Case ◽  
Two Parameters

This article develops an asymptotic theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the asymptotic theory for the persistence parameter depends critically on its sign, corresponding asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered, and strong consistency and the asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart (2010) is also considered.

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