For a small buffer queueing system fed by a large class of traffic processes we show that the single server queue and the associated sample paths behave as if fed by marked Poisson traffic; in a large deviations limit, for a system fed by many flows. The timescale upon which events occur in this setting tends to zero, hence we study a limit on the log moment generating function as time tends to...

Motivated by experimental observations of active (motor-driven) intracellular transport in neuronal dendrites, we analyze a stochastic model of directed intermittent search on a tree network. A particle injected from the cell body or soma into the primary branch of the dendritic tree randomly switches between a stationary search phase and a mobile nonsearch phase that is biased in the forward d...

We consider the intensity-based approach for the modeling of default times of one or more companies. In this approach the default times are defined as the jump times of a Cox process, which is a Poisson process conditional on the realization of its intensity. We assume that the intensity follows the Cox-Ingersoll-Ross model. This model allows one to calculate survival probabilities and prices o...

The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent HyperErlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, haza...

The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.

In this article, the concept and definitions of Fractional Order Moment (FOM) Cumulant (FOC) are proposed, which is based on fractional derivative order Moment-generating function Cumulant-generating stochastic processes. The moment cumulant defined an expanded set from positive integer to whole real. This development not only provides a new technology for signal processing, also complements ex...

We prove Andrews-Beck type congruences for overpartitions concerning the $D$-rank and $M_2$-rank. To congruences, we establish generating function weighted (respectively, $M_2$-rank) moment of find a connection with second overpartitions.

An approach to produce a model for the data generating distribution is the well-known maximum entropy method. In this approach, the partial knowledge about the data generating distribution is formulated in terms of a set of information constraints, usually moment constraints, and the inference is based on the model that maximizes Shannon’s entropy under these constraints. In this paper we inves...