scholarly journals Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Alessandra Bianchi ◽  
Massimo Campanino ◽  
Irene Crimaldi
Keyword(s):  
Brownian Motion ◽  
Asymptotic Normality ◽  
Allan Variance ◽  
Hurst Parameter ◽  
Regression Estimator ◽  
Traffic Data ◽  
Parameter Estimator ◽  
Signal Process ◽  
Rigorous Study ◽  
Memory Parameter

In order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed. Finally, we discuss its connection with the wavelets estimators.

Moderate deviation for parameter estimator in the stochastic parabolic equations with additive fractional Brownian motion

2014 ◽  
Vol 14 (03) ◽  
pp. 1450002
Author(s):  
Jiang Hui
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Fractional Brownian Motion ◽  
Parabolic Equations ◽  
Moderate Deviation ◽  
Hurst Parameter ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Parameter Estimator ◽  
Asymptotic Behaviors

In this paper, we study the asymptotic behaviors of parameter estimator in a diagonalizable stochastic evolution equation driven by additive fractional Brownian motion with Hurst parameter H ∈ [½, 1). The moderate deviation for this estimator can be obtained.

scholarly journals Maximum Likelihood Estimation in the Fractional Vasicek Model

2017 ◽  
Vol 56 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Stanislav Lohvinenko ◽  
Kostiantyn Ralchenko
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Hurst Parameter ◽  
Unknown Parameters ◽  
Vasicek Model ◽  
Consistency And Asymptotic Normality

We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

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

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