On a Berry-Esseen type bound for the maximum likelihood estimator of a parameter for some stochastic partial differential equations.
On adaptive control of Markov chains using nonparametric estimation
Two adaptive procedures for controlled Markov chains which are based on a nonparametric window estimation are shown.
On estimating the diffusion coefficient
On estimating the diffusion coefficient [Abstract of thesis]
On estimating the diffusion coefficient : parametric versus nonparametric
On estimating the memory for finitarily markovian processes
On invariant density estimation for ergodic diffusion processes.
We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.
On minimax sequential procedures for exponential families of stochastic processes
The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of...
On perturbations of strongly admissible prior distributions
On Regression Models with Non-Square Integrable Martingale-Like Errors
On the approximation of some optimal sequential plan
On the Bayesian estimation for the stationary Neyman-Scott point processes
The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good as the fast...
On the error exponent for ergodic Markov source
On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
On the estimation of the drift coefficient in diffusion processes with random stopping times.
This paper considers stochastic differential equations with solutions which are multidimensional diffusion processes with drift coefficient depending on a parametric vector θ. By considering a trajectory observed up to a stopping time, the maximum likelihood estimator for θ has been obtained and its consistency and asymptotic normality have been proved.
On the law of large numbers for continuous-time martingales and applications to statistics.
In order to develop a general criterion for proving strong consistency of estimators in Statistics of stochastic processes, we study an extension, to the continuous-time case, of the strong law of large numbers for discrete time square integrable martingales (e.g. Neveu, 1965, 1972). Applications to estimation in diffusion models are given.
On-line nonparametric estimation.
A survey of some recent results on nonparametric on-line estimation is presented. The first result deals with an on-line estimation for a smooth signal S(t) in the classic 'signal plus Gaussian white noise' model. Then an analogous on-line estimator for the regression estimation problem with equidistant design is described and justified. Finally some preliminary results related to the on-line estimation for the diffusion observed process are described.
Optimal trend estimation in geometric asset price models
In the general geometric asset price model, the asset price P(t) at time t satisfies the relation , t ∈ [0,T], where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility. The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient...