In this dissertation, we are mainly concerned with the sum of random exponentials. Here, the random variables are independent and identically distributed. Another distinc[...]

Small cells are introduced as one of the key technologies of the new generation (5G) mobile networks. Among the existing small cell technologies, femtocells drew more res[...]

We introduce two different reaction diffusion models: evolution of one-cell populations in the presence of mitosis and continuous contact model.In the first model we cons[...]

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[...]

In this thesis, we introduce a methodology for the simulation and parameter estimation of multivariate tempered stable distributions. Using the fact that tempered stable [...]

In this dissertation, we consider European-style commodity options and futures options where the logarithm of the underlying commodity price dynamics is governed by the r[...]

Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) are widely used in image and data compression applications. To process the DCT or DST of a signal a port[...]

We study the behavior of branching process in a random environment on trees in the critical, subcritical and supercritical case. We are interested in the case when both t[...]

This dissertation contains several new results concerning Moser-type optimal stopping problems. In the simplest case we consider sequence of independent uniformly distrib[...]