The computing of stochastic bounds has become an efficient technique to obtain performance predictions for computer systems by the mean of Markovian models. However, the quality of these bounds may be affected by several properties related not only to how to use the technique but also to the Markovian model itself. On the other hand, multiprocessor systems have become an efficient and widely us...

We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, (Δx2(t))∝t(2+λ), with λ∼1-3 is detected in tilted washboard potentials before it ends up in a ballistic asymptotic regime. We r...

We study a portfolio selection problem in a continuous-time Markovian regimeswitching model. The market in this model is, in general, incomplete. We adopt a method to complete the market based on an enlargement of the market using a set of geometric Markovian jump securities. We solve the portfolio selection problem in the enlarged market for a power utility and a logarithmic utility. Closed-fo...

Independent cascade (IC) model is a widely used influence propagation for social networks. In this paper, we incorporate the concept and techniques from causal inference to study identifiability of parameters observational data in extended IC with unobserved confounding factors, which models more realistic scenarios but rarely studied modeling before. We provide conditions or unidentifiability ...

We investigate the behavior of stochastic bistable and excitable dynamics based on a discrete state modeling. In addition to the well known Markovian two state model for bistable dynamics we introduce a non Markovian three state model for excitable systems. Its relative simplicity compared to stochastic models of excitable dynamics with continuous phase space allows to obtain analytical results...

We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is both computationally efficient and numerically stable. The algorithms we present are also physically transparent and so allow us to extend this method from the ...

This paper presents a recursive method of computing the distribution of the number of successes in a sequence of binary trials that are Markovian of a general order. Waiting-time distributions are also obtained. Recurrence relations among probabilities of partitioned events are used to compute the desired probabilities. An advantage of computing the probabilities in the manner given is that the...

Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...

Starting with the Wigner function formulation for beam wave propagation in Hölder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and converges to a Gaussian Markovian model which is characterized the martingale problem associated to a stochastic differential-integral equation of the Ito type. In the geome...

In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces local observables. The dynamics is described by general Markovian master equation based on which Hamiltonian identification problem can be formulated as minimizing distance between real observables and those predicted equation. then learned with descen...