Parameter estimation of one-dimensional diffusion process by minimum Hellinger distance method

2013 ◽  
Vol 21 (4) ◽  
Author(s):  
Julien Apala N'drin ◽  
Ouagnina Hili
Keyword(s):  
Parameter Estimation ◽  
Diffusion Process ◽  
Hellinger Distance ◽  
Distance Method ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Minimum Hellinger Distance

scholarly journals Minimum Hellinger Distance Estimation of a Univariate GARCH Process

2017 ◽  
Vol 9 (3) ◽  
pp. 80
Author(s):  
Roger Kadjo ◽  
Ouagnina Hili ◽  
Aubin N'dri
Keyword(s):  
Asymptotic Normality ◽  
Almost Sure Convergence ◽  
Distance Estimation ◽  
Hellinger Distance ◽  
Distance Method ◽  
Garch Process ◽  
Minimum Hellinger Distance ◽  
Distance Estimator

In this paper, we determine the Minimum Hellinger Distance estimator of a stationary GARCH process. We construct an estimator of the parameters based on the minimum Hellinger distance method. Under conditions which ensure the $\phi$-mixing of the GARCH process, we establish the almost sure convergence and the asymptotic normality of the estimator.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

Recursive parameter estimation in the trend coefficient of a diffusion process

2010 ◽  
Vol 17 (4) ◽  
pp. 683-704
Author(s):  
Nanuli Lazrieva ◽  
Teimuraz Toronjadze
Keyword(s):  
Parameter Estimation ◽  
Diffusion Process ◽  
Asymptotic Properties ◽  
Recursive Estimation ◽  
Dimensional Parameter ◽  
One Dimensional ◽  
Recursive Parameter Estimation ◽  
Special Cases ◽  
Trend Coefficient ◽  
Recursive Estimators

Abstract The recursive estimation problem of a one-dimensional parameter in the trend coefficient of a diffusion process is considered. The asymptotic properties of recursive estimators are derived, based on the results on the asymptotic behaviour of a Robbins–Monro type SDE. Various special cases are considered.

Co-dimension Two Bifurcations in the Presence of Noise

1991 ◽  
Vol 58 (1) ◽  
pp. 259-265 ◽  
Author(s):  
N. Sri Namachchivaya
Keyword(s):  
Normal Form ◽  
Diffusion Process ◽  
Stochastic Averaging ◽  
Singularly Perturbed ◽  
Stability Conditions ◽  
Exit Times ◽  
Double Zero ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Stochastic Bifurcations

Some results pertaining to co-dimension two stochastic bifurcations are presented. The normal form associated with non-semi-simple double-zero eigenvalues is considered. The method of stochastic averaging applicable for singularly perturbed stochastic differential equations is used to further reduce the problem to a one dimensional diffusion process. Probability density, most probable values, stability conditions in probability, and mean exit times are obtained for the reduced system.

Sign in / Sign up

Export Citation Format

Share Document