Showing papers by "Enzo Orsingher published in 1997"
11 citations
TL;DR: In this article, it was shown that the conditional and unconditional distributions of the position of a uniformly accelerated particle with Poisson-paced changes of its acceleration tend in distribution to a normal variate asn goes to infinity.
Abstract: In this paper, the process {X(t); t>0}, representing the position of a uniformly accelerated particle (with Poisson-paced) changes of its acceleration, is studied. It is shown that the distribution ofX(t) (suitably normalized), conditionally on the numbern of changes of acceleration, tends in distribution to a normal variate asn goes to infinity. The asymptotic normality of the unconditional distribution ofX(t) for large values oft is also shown. The study of these limiting distributions is motivated by the difficulty of evaluating exactly the conditional and unconditional probability laws ofX(t). In fact, the results obtained in this paper permit us to give useful approximations of the probability distributions of the position of the particle.
2 citations
TL;DR: In this paper, the third-order equations governing the distributions of the three-valued telegraph process were derived and recurrence relationships for them were obtained by solving suitable initial value problems.
Abstract: In this paper the integrated three-valued telegraph process X= X(t), t > 0 is examined. In particular, the third-order equations governing the distributions Pr{X(t) 0, (where N(t) denotes the number of changes of the telegraph process up to time t) are derived and recurrence relationships for them are obtained by solving suitable initialvalue problems. These recurrence formulas are related to the Fourier transform of the conditional distributions and are used to obtain explicit results for small values of k. The conditional mean values E{X(t) I N(t)= k, V(O) =j}, k > 0, j= 1, 0,- 1 (where V(0) denotes the initial velocity of motions) are obtained and discussed.
2 citations