arXiv subjects
Publications and source records attributed to Andrea Monsellato.
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give an explicit expression of the transition probabilities.
Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \cite{PolyaUrn}, starting from a particular type of recurrence differential equation it is used an analytic approach to recover explicit probabilities and generating function. Note that this kind of recurrence differential equations often appear in Polya Urn context \cite{PolyaUrn}.
Consider the following birth and death process with the following infinitesimal transition probabilities λ(k) =λ/(1+k) and μ(k) = μk with λ,μ> 0. This process has known as a discouragement queue [5]. Although from the theoretical point of view the problem of the determination of the transition functions has been solved [4], the explicit form of them is not present in literature. We have solved this problem assuming that the solution is representable by a Taylor series, under the initial condition that the process starts to state zero. We discuss also the same problem for the embedded chain and using direct computation we obtain a recursive formula for the transient distribution.
Consider a pure birth process with intensities λ(k) =1/(1+k), with k=0,1,2,..., we show that the subordinated chain is assimilable to a Bernoullian scheme with dependent successes probabilities, also we show a direct link with a degenerate Polya urn replacement scheme \cite{Janson}. We compute explicitly transition probabilities, by generating function method, of the subordinated chain and give some interesting bounds using the "centering sequence" approach proposed by MacDiarmid \cite{McDiarmidcentering}.
This paper is a short summary of the main results in the thesis [1]. Based on the P2P paradigm we construct a stochastic model for a live media streaming content delivery network. Starting from the behavior of the out degree process of each node we analyze the evolution of the resulting random graph. For the out degree process we provide an iterative formula for the distribution probabilities and calculate an explicit expression for the transient distribution. Moreover we discuss the steady state distribution and the problem of local disconnections.