A fast estimation algorithm on the Hurst parameter of discrete-time fractional Brownian motion

2002 ◽  
Vol 50 (3) ◽  
pp. 554-559 ◽  
Author(s):  
Yen-Ching Chang ◽  
Shyang Chang
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Estimation Algorithm ◽  
Hurst Parameter ◽  
Fast Estimation

scholarly journals Least Squares Estimation forα-Fractional Bridge with Discrete Observations

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guangjun Shen ◽  
Xiuwei Yin
Keyword(s):  
Brownian Motion ◽  
Least Squares ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Unknown Parameter ◽  
Least Squares Estimation ◽  
Least Squares Estimator ◽  
Hurst Parameter ◽  
Discrete Observations ◽  
Observation Window

We consider a fractional bridge defined asdXt=-α(Xt/(T-t))dt+dBtH,  0≤t<T, whereBHis a fractional Brownian motion of Hurst parameterH>1/2and parameterα>0is unknown. We are interested in the problem of estimating the unknown parameterα>0. Assume that the process is observed at discrete timeti=iΔn,  i=0,…,n, andTn=nΔndenotes the length of the “observation window.” We construct a least squares estimatorα^nofαwhich is consistent; namely,α^nconverges toαin probability asn→∞.

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 Discrete-Time Inference for Slow-Fast Systems Driven by Fractional Brownian Motion

2021 ◽  
Vol 19 (3) ◽  
pp. 1333-1366
Author(s):  
Solesne Bourguin ◽  
Siragan Gailus ◽  
Konstantinos Spiliopoulos
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Discrete Time

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

Renormalization Group Method for Singular Perturbed Systems Driven by Fractional Brownian Motion

2019 ◽  
Author(s):  
Lihong Guo ◽  
Shaoyun Shi ◽  
YangQuan Chen
Keyword(s):  
Brownian Motion ◽  
Renormalization Group ◽  
Fractional Brownian Motion ◽  
High Probability ◽  
Large Time ◽  
Approximate Solutions ◽  
Hurst Parameter ◽  
Group Method ◽  
Renormalization Group Method ◽  
Perturbed Systems

Abstract In this article, we use the renormalization group method to study the approximate solution of stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H∈12,1. We derive a related reduced system, which we use to construct the separate scale approximation solutions. It is shown that the approximate solutions remain valid with high probability on large time scales. We also expect that our general approach can be applied to the fields of physics, finance, and engineering, etc.

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