Parameter estimation in stochastic systems: some recent results and applications
Parametric inference for mixed models defined by stochastic differential equations
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...
Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process
Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when t → ∞. The main point of our work is that we do not suppose the process to be in...
Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process
Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when t → ∞. The main point of our work is that we do not suppose the process to be in...
Plug-in estimators for higher-order transition densities in autoregression
In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator....
Polynomial deviation bounds for recurrent Harris processes having general state space
Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc et al. [Stoc. Proc. Appl. 119, (2009) 897–923] introduced verifiable conditions in terms of a supermartingale property implying an explicit control of modulated moments of hitting times. We show how this control can be translated into a control of polynomial moments of abstract regeneration times which are obtained by using the regeneration method of Nummelin, extended to the time-continuous...
Process parameter prediction via markov models of sub-activities
This work aims to fill a lacunae in the project-oriented production systems literature providing a formal analytic description of the rework effects formulae and the determination of the extended design time due to a certain degree of overlapping in a pair of activities. It is made through the utilization of concepts of workflow construction with hidden (semi) Markov models theory and establishing a way to disaggregate activities into sub-activities, in order to determine the activity parameters...
Prognosis and optimization of homogeneous Markov message handling networks
Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchic networks is found a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of the system design and management are discussed, as well as a program product 5P (Program for Prognosis of Performance Parameters and Problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical...
Propriété asymptotique d’un modèle statistique pour une chaîne de Markov à valeurs dans