Limit theorems for a class of integral functionals driven by fractional Brownian motion

2021 ◽  
pp. 1-23
Author(s):  
Xiaoyu Xia ◽  
Litan Yan
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Limit Theorems ◽  
Integral Functionals

SOME LIMIT THEOREMS ON THE INCREMENTS OF A MULTI-PARAMETER FRACTIONAL BROWNIAN MOTION

2001 ◽  
Vol 19 (4) ◽  
pp. 499-517 ◽  
Author(s):  
Zheng-Yan Lin ◽  
Yong-Kab Choi ◽  
Kyo-Shin Hwang
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Limit Theorems

scholarly journals On some statistics of fractional Brownian motion

2021 ◽  
pp. 131-138
Author(s):  
Viktor Bondarenko
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hurst Exponent ◽  
Limit Theorems ◽  
Goodness Of Fit ◽  
Mean Square ◽  
One Step ◽  
Optimal Forecasting

Fractional Brownian motion as a method for estimating the parameters of a stochastic process by variance and one-step increment covariance is proposed and substantiated. The root-mean-square consistency of the constructed estimates has been proven. The obtained results complement and generalize the consequences of limit theorems for fractional Brownian motion, that have been proved in the number of articles. The necessity to estimate the variance is caused by the absence of a base unit of time and the estimation of the covariance allows one to determine the Hurst exponent. The established results let the known limit theorems to be used to construct goodness-of-fit criteria for the hypothesis “the observed time series is a transformation of fractional Brownian motion” and to estimate the error of optimal forecasting for time series.

scholarly journals Limit theorems for a quadratic variation of Gaussian processes

2011 ◽  
Vol 16 (4) ◽  
pp. 435-452 ◽  
Author(s):  
Raimondas Malukas
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Fractional Brownian Motion ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Quadratic Variation

In the paper a weighted quadratic variation based on a sequence of partitions for a class of Gaussian processes is considered. Conditions on the sequence of partitions and the process are established for the quadratic variation to converge almost surely and for a central limit theorem to be true. Also applications to bifractional and sub-fractional Brownian motion and the estimation of their parameters are provided.

On limit theorems of some extensions of fractional Brownian motion and their additive functionals

2017 ◽  
Vol 17 (03) ◽  
pp. 1750022
Author(s):  
M. Ait Ouahra ◽  
S. Moussaten ◽  
A. Sghir
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Limit Theorems ◽  
Fractional Derivatives ◽  
Slowly Varying Function ◽  
Bifractional Brownian Motion ◽  
Additive Functionals ◽  
Subfractional Brownian Motion

This paper is divided into two parts. The first deals with some limit theorems to certain extensions of fractional Brownian motion like: bifractional Brownian motion, subfractional Brownian motion and weighted fractional Brownian motion. In the second part we give the similar results of their continuous additive functionals; more precisely, local time and its fractional derivatives involving slowly varying function.

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