13 research outputs found
Large Deviations Principle for a Large Class of One-Dimensional Markov Processes
We study the large deviations principle for one dimensional, continuous,
homogeneous, strong Markov processes that do not necessarily behave locally as
a Wiener process. Any strong Markov process in that is
continuous with probability one, under some minimal regularity conditions, is
governed by a generalized elliptic operator , where and are
two strictly increasing functions, is right continuous and is
continuous. In this paper, we study large deviations principle for Markov
processes whose infinitesimal generator is where
. This result generalizes the classical large deviations
results for a large class of one dimensional "classical" stochastic processes.
Moreover, we consider reaction-diffusion equations governed by a generalized
operator . We apply our results to the problem of wave front
propagation for these type of reaction-diffusion equations.Comment: 23 page
An almost sure invariance principle for the empirical distribution function of mixing random variables
On Conditional Density Estimation
With the aim of mitigating the possible problem of negativity in the estimation of the conditional density function, we introduce a so-called re-weighted Nadaraya-Watson (RNW) estimator. The proposed RNW estimator is constructed by a slight modification of the well-known Nadaraya-Watson smoother. With a detailed asymptotic analysis, we demonstrate that the RNW smoother preserves the superior large-sample bias property of the local linear smoother of the conditional density recently proposed in the literature. As a matter of independent statistical interest, the limit distribution of the RNW estimator is also derived
Asymptotic properties for LS estimators in EV regression model with dependent errors
EV regression models, LS estimator, α-mixing sequence, Strong consistency, Asymptotic normality,