Sulla teoria dei processi stocastici indicizzati da insiemi
The behavior of a Markov network with respect to an absorbing class: the target algorithm
In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the -length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can be reduced by collapsing together those states that behave in the same way for the purposes of calculating...
Stopping Markov processes and first path on graphs
Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....
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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