ﻻ يوجد ملخص باللغة العربية
We show that any (real) generalized stochastic process over $mathbb{R}^{d}$ can be expressed as a linear transformation of a White Noise process over $mathbb{R}^{d}$. The procedure is done by using the regularity theorem for tempered distributions to obtain a mean-square continuous stochastic process which is then expressed in a Karhunen-Lo`eve expansion with respect to a convenient Hilbert space. This result also allows to conclude that any generalized stochastic process can be expressed as a series expansion of deterministic tempered distributions weighted by uncorrelated random variables with square-summable variances. A result specifying when a generalized stochastic process can be linearly transformed into a White Noise is also presented.
We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain. We consider
A continuous-time nonlinear regression model with Levy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper.
Suppose that a random variable $X$ of interest is observed perturbed by independent additive noise $Y$. This paper concerns the the least favorable perturbation $hat Y_ep$, which maximizes the prediction error $E(X-E(X|X+Y))^2$ in the class of $Y$ wi
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. T
The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better understanding