Applied Mathematics

In this dissertation, the classic one dimension orthogonal wavelet construction scheme is discussed and extended to construct Parseval's frame wavelets in high dimension [...]

We define a class of convex measures of risk whose values depend on the random variables only up to the lambda-quantiles for some given constant lambda in (0,1). For thi[...]

The Least absolute deviation combined with the Least absolute shrinkage andselection operator (LAD-LASSO) estimator can do regression shrinkage and selectionand is also r[...]

In this dissertation, we mainly discuss the image approximation methods to the reaction field and their applications to electrostatic interactions in molecular dynamics s[...]

In financial time series nonlinear effects and time-varying effects are observed. In this dissertation we propose a predictive regression model with time varying coefficients [...]

We study the topological properties of minimally generated algebras (as introduced by Koppelberg) and, particularly, the subclass of T-algebras (a notion due to Koszmid[...]

The goal of this dissertation is to give the sufficient conditions for the absence of a.c.spectrum or existence of the pure point (p.p.) spectrum for the deterministic or[...]

We present recursive algorithms to calculate invariant distributions and fundamental matrices of Markov chains specified by the "Islands & Ports'" (IP) model. The sta[...]

The central objects of the thesis are the Anderson parabolic problem and the Moser's type optimal stopping problem:(1) In the lattice parabolic Anderson problem, we study[...]

ABSTRACTIn this dissertation, firstly, I study spatial quantile regression estimation of multivariate threshold time series models. Asymptotic normality of the proposed s[...]