Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients

2017 ◽  
Vol 44 (3) ◽  
pp. 617-635 ◽  
Author(s):  
Abdelkamel Alj ◽  
Rajae Azrak ◽  
Christophe Ley ◽  
Guy Mélard
Keyword(s):  
Asymptotic Properties ◽  
Time Dependent

Exact and asymptotic solutions to a PDE that arises in time-dependent queues

2000 ◽  
Vol 32 (1) ◽  
pp. 256-283 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Limit Theorems ◽  
Asymptotic Properties ◽  
Mathematical Physics ◽  
Linear Functions ◽  
Time Dependent ◽  
One Dimension ◽  
Asymptotic Results ◽  
Piecewise Constant ◽  
Space And Time ◽  
Diffusion Problems

We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

Exact and asymptotic solutions to a PDE that arises in time-dependent queues

2000 ◽  
Vol 32 (01) ◽  
pp. 256-283 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Limit Theorems ◽  
Asymptotic Properties ◽  
Mathematical Physics ◽  
Linear Functions ◽  
Time Dependent ◽  
One Dimension ◽  
Asymptotic Results ◽  
Piecewise Constant ◽  
Space And Time ◽  
Diffusion Problems

We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

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