Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Lévy processes with periodic mean

2019 ◽  
Vol 14 (6) ◽  
pp. 1281-1302
Author(s):  
Guangjun Shen ◽  
Qian Yu ◽  
Yunmeng Li
Keyword(s):  
Least Squares ◽  
Lévy Processes ◽  
Levy Processes ◽  
Least Squares Estimator

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.

On correlating Lévy processes

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

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

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