Stability results for a diffusive nonlinear deterministic epidemic model
Si stabilisce un risultato di stabilità asintotica per la soluzione di equilibrio di una equazione semilineare di evoluzione che descrive un modello epidemico.
Contributions to stochastic compartmental analysis
Viene affrontato lo studio della formalizzazione stocastica dei modelli compartimentali proposta da Matis e Hartley [5]. La risoluzione in forma chiusa per la funzione generatrice di probabilità (p.g.f.) mette in evidenza il ruolo dominante della matrice compartimentale nella evoluzione del sistema, il che consente di sfruttare sistematicamente risultati originati dalla corrispondente teoria deterministica. Si ottiene una serie di implicazioni sul tipo di distribuzione probabilistica delle particelle...
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Integration in a dynamical stochastic geometric framework
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
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