We develop the asymptotic theory for the realised power variation of the processes X = f • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of...

The use of computer modeling is fast increasing in almost everyscientific, engineering and business arena. This dissertationinvestigates some challenging issues in design, modeling andanalysis of computer experiments, which will consist of four majorparts. In the first part, a new approach is...

This paper proposes a new Bayesian approach for estimating, nonparametrically, parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior distribution we propose the posterior mean as an estimator and prove consistency,...

This paper proposes a new minimum distance methodology for the estimation of ARFIMA processes with Gaussian and non-Gaussian errors. The main advantage of this method is that it allows for a computationally efficient estimation when the long-memory parameter is in the interval d∈(−12,12)....

We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields W(t,x) and for the solution u(t,y) of the stochastic heat equation with...

In energy and environment field models are constructed, in general, based on well-defined physical phenomena and properties. Calibration and uncertainty analysis hold a particular interest because models represent a simplification of reality and, therefore, it is necessary to quantify to what...

The aim of this work is to prove the existence of a positive solution for a class of generalized delay logistic equations with multifractional noise. To do this, a method of semimartingale approximation is introduced.