scholarly journals Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations

2017 ◽  
Vol 60 (6) ◽  
pp. 2253-2271 ◽  
Author(s):  
Guangjun Shen ◽  
Qian Yu
Keyword(s):  
Least Squares ◽  
Lévy Processes ◽  
Levy Processes ◽  
Least Squares Estimator ◽  
Discrete Observations

scholarly journals Least Squares Estimator for Vasicek Model Driven by Fractional Levy Processes

2018 ◽  
Vol 14 (2) ◽  
pp. 8013-8024
Author(s):  
Qingbo Wang ◽  
Xiuwei Yin
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Estimation Problem ◽  
Least Squares Estimator ◽  
Parameter Estimation Problem ◽  
Vasicek Model ◽  
Model Driven

In this paper, we consider parameter estimation problem for Vasicek model driven by fractional lévy processes defined We construct least squares estimator for drift parameters based on time?continuous observations, the consistency and asymptotic distribution of these estimators are studied in the non?ergodic case. In contrast to the fractional Vasicek model, it can be regarded as a Lévy generalization of fractional Vasicek model.

Least squares estimator for stochastic differential equations driven by small fractional Lévy noises from discrete observations

2021 ◽  
pp. 2150047
Author(s):  
Qian Yu ◽  
Guangjun Shen ◽  
Wentao Xu
Keyword(s):  
Asymptotic Behavior ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Dispersion Coefficient ◽  
Least Squares Estimator ◽  
Regularity Conditions ◽  
Discrete Observations ◽  
Small Dispersion

In this paper, we consider the problem of parameter estimation for stochastic differential equations with small fractional Lévy noises, based on discrete observations. Under certain regularity conditions on drift function, the consistency of least squares estimation has been established as a small dispersion coefficient [Formula: see text] and the number of discrete points [Formula: see text] simultaneously. We also obtain the asymptotic behavior of the estimator.

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→∞.

On correlating Lévy processes

2010 ◽  
Vol 13 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Ernst Eberlein ◽  
Dilip Madan
Keyword(s):  
Lévy Processes ◽  
Levy Processes
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