Calibration of the Modified Geometric Ornstein-Uhlenbeck Process Through the Maximum Log-Likelihood Method. An Example with Gold Prices (Calibraciin del Proceso Ornstein-Uhlenbeck Geommtrico Modificado a travvs del MMtodo de MMxima Log-Verosimilitud. Un Ejemplo con los Precios del Oro)

2017 ◽  
Author(s):  
Carlos Mejia
Keyword(s):  
Likelihood Method ◽  
Uhlenbeck Process ◽  
Log Likelihood ◽  
Ornstein Uhlenbeck Process

On bayes approach to univariate global optimization

2012 ◽  
Author(s):  
Leonidas Sakalauskas ◽  
Jurgis Susinskas
Keyword(s):  
Computer Simulation ◽  
Global Optimization ◽  
Objective Function ◽  
Optimization Method ◽  
Continuous Functions ◽  
Likelihood Method ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Learning Set ◽  
The Bayesian Approach

In this paper the Bayesian approach to global optimization of univariate continuous functions is developed, when the objective function is modelled by Ornstein-Uhlenbeck process. The parameters of model of function to be optimised are calibrated by maximal likelihood method using the learning set. The resulting optimization algorithm is rather simple and consists of reselection of values of expected step utility function, which maximizes at each step the expected increment of minimal observed value of the objective function. The convergence of method developed is studied by theoretical and experimental way. Efficiency of the Bayes optimization method created is studied by computer simulation, too.

Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift

2020 ◽  
Vol 21 (02) ◽  
pp. 2150027
Author(s):  
Hui Jiang ◽  
Hui Liu
Keyword(s):  
Likelihood Ratio ◽  
Decay Rates ◽  
Moderate Deviations ◽  
Uhlenbeck Process ◽  
Testing Problem ◽  
Analysis Techniques ◽  
Log Likelihood ◽  
Ornstein Uhlenbeck Process ◽  
Deviation Inequalities ◽  
Error Probabilities

For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-[Formula: see text] convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.

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

On the reflected Ornstein–Uhlenbeck process with catastrophes

2012 ◽  
Vol 218 (23) ◽  
pp. 11570-11582 ◽  
Author(s):  
V. Giorno ◽  
A.G. Nobile ◽  
R. di Cesare
Keyword(s):  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process
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