This paper presents a mathematical model for designing cellular manufacturing systems (CMSs) solved by genetic algorithms. This model assumes a dynamic production, a stochastic demand, routing flexibility, and machine flexibility. CMS is an application of group technology (GT) for clustering parts and machines by means of their operational and / or apparent form similarity in different aspects ...

We extend the folk theorem of repeated games to two settings in which players’ information about others’ play arrives with stochastic lags. In our first model, signals are almost-perfect if and when they do arrive, that is, each player either observes an almost-perfect signal of period-t play with some lag or else never sees a signal of period-t play. The second model has the same lag structure...

Pickands constants play an important role in the exact asymptotic of extreme values for Gaussian stochastic processes. By the generalized Pickands constant Hη we mean the limit Hη = lim T→∞ Hη(T ) T , where Hη(T ) = IE exp ( maxt∈[0,T ] (√ 2η(t)− σ2 η(t) )) and η(t) is a centered Gaussian process with stationary increments and variance function σ2 η(t). Under some mild conditions on σ2 η(t) we ...

The parabolic Anderson problem is the Cauchy problem for the heat equation ∂tu(t, z) = ∆u(t, z) + ξ(z)u(t, z) on (0,∞) × Z with random potential (ξ(z) : z ∈ Z). We consider independent and identically distributed potential variables, such that Prob(ξ(z) > x) decays polynomially as x ↑ ∞. If u is initially localised in the origin, i.e. if u(0, x) = 1l0(x), we show that, at any large time t, the ...

Abstract. We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the classical logistic model [22] when the carrying capacity is large. Being discrete and stochastic, however, our population nonetheless goes extinct in fi...

This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochas...

We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recen...