Sentence examples for based on discrete observations from inspiring English sources
From a practical standpoint, it is more realistic and amusing to consider asymptotic properties of the estimator based on discrete observations of (X_{t}).
So, recently in the literature, the statistical inference for diffusion processes based on discrete observations has often been of concern; for example, see [3 6] and its references for parametric estimation, see [7 9] and the references therein for a semi-parametric estimation and see [10 16] and the references therein for a nonparametric estimation.
It is more realistic and interesting to consider the parameter estimation for diffusion processes based on discrete observation, since the actual data may be obtained discretely.
The mean-square and the almost sure convergence of these estimators based on discrete-time observations are provided.
State-feedback controls based on discrete-time observations are designed in the drift and diffusion parts of the system.
In this paper, new variable bandwidth nonparametric robust estimators for the drift function and diffusion function of diffusion processes based on discrete-time observations are devised.
As for a parameter estimation based on discrete-time observations, Sørensen [17] gave an excellent survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time.
Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations.
In 2013, Mao [24] initiated the study on the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations.
Our attention is focused on the design of a feedback controller based on discrete-time state observations such that, for all admissible uncertainties, the closed-loop system is robustly exponentially stable in the mean square, independent of the time delay.
In 2013, Mao [24] initiated the study of the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations, which cost less and are more realistic.
