Uniform Rate of Weak Convergence of the Minimum Contrast Estimator in the Ornstein–Uhlenbeck Process

2008 ◽  
Vol 12 (3) ◽  
pp. 323-334 ◽  
Author(s):  
Jaya P. N. Bishwal
Keyword(s):  
Weak Convergence ◽  
Uhlenbeck Process ◽  
Minimum Contrast Estimator ◽  
Uniform Rate ◽  
Minimum Contrast ◽  
Ornstein Uhlenbeck Process

Weak convergence of an autoregressive process used in modeling population growth

1982 ◽  
Vol 19 (2) ◽  
pp. 450-455 ◽  
Author(s):  
W. G. Cumberland ◽  
Z. M. Sykes
Keyword(s):  
Weak Convergence ◽  
Population Growth ◽  
Autoregressive Process ◽  
Vital Rates ◽  
Uhlenbeck Process ◽  
First Order ◽  
Ornstein Uhlenbeck Process

Under simple limiting conditions a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process. The result is discussed in the context of modeling vital rates for biological populations in random environments.

Weak convergence of an autoregressive process used in modeling population growth

1982 ◽  
Vol 19 (02) ◽  
pp. 450-455 ◽  
Author(s):  
W. G. Cumberland ◽  
Z. M. Sykes
Keyword(s):  
Weak Convergence ◽  
Population Growth ◽  
Autoregressive Process ◽  
Vital Rates ◽  
Uhlenbeck Process ◽  
First Order ◽  
Ornstein Uhlenbeck Process

Under simple limiting conditions a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process. The result is discussed in the context of modeling vital rates for biological populations in random environments.

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
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