In this paper, we consider the dividend payments prior to absolute ruin in a Markovian regime-switching risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying Markov jump process. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the n th moment of the disc...

We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics for the stationary probabilities on the coordinate axis. This refines the asymptotic results in the literature, and completely solves the tail asymptotic pro...

Abstract. We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called quasimock theta functions, while a fourth specialization gives quasimodular forms. We then define a two-parameter generalization of Andrews’ smalle...

A continuous case of new density function called harmonic probability density function (HPDF) is structured using mathematical method. The mean and variance of this probability function is presented using both the definition and moment generating function. A discussion has started on many other connections that may exist between this new model and its applications in geometry, probability, and ...

Rate outage probability is an important performance metric to measure the level of quality of service (QoS) in the Generation (4G) broadband access networks. Thus, in this paper, we calculate a closed form expression of the rate outage probability for a given user in a down-link multi-hop OFDMAbased system encountered as a result of links’ channel variations. The channel random behavior on diff...

of Long Term Evolution (LTE) for indoor coverage extension. Heterogeneous networks in which femto and pico-cells are overlaid onto macro-cells are extensively discussed. In order to maintain reliable service of macro-cells, it is important to mitigate destructive femto-femto (co-channel) and femto-macro (adjacent or cross channel) cell interferences respectively. This paper presents the perform...

The signal-to-noise-plus-interference ratio (SINR) outage probability is one of the key performance parameters of a wireless cellular network, and its analytical as well as numerical evaluation has occupied many researchers. Recently, the introduction of stochastic geometric modeling of cellular networks has brought the outage problem to the forefront again. A popular and powerful approach is t...