scholarly journals The precise asymptotic behavior of parameter estimators in Ornstein–Uhlenbeck process

2011 ◽  
Vol 382 (1) ◽  
pp. 367-382
Author(s):  
Hui Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Parameter Estimators ◽  
Precise Asymptotic

An absorption probability for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (3) ◽  
pp. 595-599 ◽  
Author(s):  
John P. Dirkse
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Closed Form ◽  
Asymptotic Expression ◽  
Uhlenbeck Process ◽  
Absorption Probability ◽  
Optional Stopping ◽  
Ornstein Uhlenbeck Process ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

An asymptotic expression for an absorption probability for the Ornstein-Uhlenbeck process is presented along with an application of the result to a problem in optional stopping. The relation of this result to the asymptotic behavior of a weighted Kolmogorov-Smirnov statistic is also discussed. Sweet and Hardin (1970) derive an exact solution (not in closed form) for this same problem.

An absorption probability for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (03) ◽  
pp. 595-599
Author(s):  
John P. Dirkse
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Closed Form ◽  
Asymptotic Expression ◽  
Uhlenbeck Process ◽  
Absorption Probability ◽  
Optional Stopping ◽  
Ornstein Uhlenbeck Process ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

An asymptotic expression for an absorption probability for the Ornstein-Uhlenbeck process is presented along with an application of the result to a problem in optional stopping. The relation of this result to the asymptotic behavior of a weighted Kolmogorov-Smirnov statistic is also discussed. Sweet and Hardin (1970) derive an exact solution (not in closed form) for this same problem.

First-passage-time density and moments of the ornstein-uhlenbeck process

1988 ◽  
Vol 25 (01) ◽  
pp. 43-57 ◽  
Author(s):  
Luigi M. Ricciardi ◽  
Shunsuke Sato
Keyword(s):  
Asymptotic Behavior ◽  
First Passage Time ◽  
Passage Time ◽  
Exponential Functions ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Density ◽  
Single Exponential ◽  
Explicit Expressions

A detailed study of the asymptotic behavior of the first-passage-time p.d.f. and its moments is carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant boundary. Explicit expressions are determined which include those earlier discussed by Sato [15] and by Nobile et al. [9]. In particular, it is shown that the first-passage-time p.d.f. can be expressed as the sum of exponential functions with negative exponents and that the latter reduces to a single exponential density as time increases, irrespective of the chosen boundary. The explicit expressions obtained for the first-passage-time moments of any order appear to be particularly suitable for computation purposes.

First-passage-time density and moments of the ornstein-uhlenbeck process

1988 ◽  
Vol 25 (1) ◽  
pp. 43-57 ◽  
Author(s):  
Luigi M. Ricciardi ◽  
Shunsuke Sato
Keyword(s):  
Asymptotic Behavior ◽  
First Passage Time ◽  
Passage Time ◽  
Exponential Functions ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Density ◽  
Single Exponential ◽  
Explicit Expressions

A detailed study of the asymptotic behavior of the first-passage-time p.d.f. and its moments is carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant boundary. Explicit expressions are determined which include those earlier discussed by Sato [15] and by Nobile et al. [9]. In particular, it is shown that the first-passage-time p.d.f. can be expressed as the sum of exponential functions with negative exponents and that the latter reduces to a single exponential density as time increases, irrespective of the chosen boundary. The explicit expressions obtained for the first-passage-time moments of any order appear to be particularly suitable for computation purposes.

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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