Estimation of all parameters in the reflected Ornstein–Uhlenbeck process from discrete observations

2021 ◽  
Vol 174 ◽  
pp. 109099
Author(s):  
Yaozhong Hu ◽  
Yuejuan Xi
Keyword(s):  
Discrete Observations ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

Berry-Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process with discrete observations

2019 ◽  
Vol 64 (3) ◽  
pp. 502-525
Author(s):  
Farez Alazemi ◽  
Farez Alazemi ◽  
Soukhana Douissi ◽  
Soukhana Douissi ◽  
Khalifa Es-Sebaiy ◽  
...  
Keyword(s):  
Discrete Observations ◽  
Parameter Estimator ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

Рассматривается задача оценивания сноса смешанного процесса Орнштейна-Уленбека на основе наблюдений в фиксированные дискретные моменты времени. С использованием исчисления Маллявена и недавнего анализа Нурдина-Пеккати исследуется асимптотическое поведение оценки. Более точно, изучаются сильная состоятельность и асимптотическое распределение оценки; установлена также скорость ее сходимости по распределению для всех $H\in(0,1)$. Более того, доказано, что в случае $H\in(0,3/4]$ оценка удовлетворяет центральной предельной теореме для сходимости почти наверное.

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Jaya Bishwal
Keyword(s):  
Normal Distribution ◽  
Hurst Exponent ◽  
Standard Normal Distribution ◽  
Discrete Observations ◽  
Uhlenbeck Process ◽  
Minimum Contrast ◽  
Contrast Estimation ◽  
Ornstein Uhlenbeck Process ◽  
Standard Normal ◽  
Drift Parameter

AbstractThe paper shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform error rate of the order O(T −1/2) for the case H > 1/2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of of weak convergence to normal distribution.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations

2017 ◽  
Vol 429 ◽  
pp. 35-45 ◽  
Author(s):  
Krzysztof Bartoszek ◽  
Sylvain Glémin ◽  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Uhlenbeck Process ◽  
Interacting Populations ◽  
Ornstein Uhlenbeck Process
Sign in / Sign up

Export Citation Format

Share Document