Showing papers by "Enzo Orsingher published in 2000"
TL;DR: In this paper, the exact joint distribution of the position of a particle performing a planar random motion with finite velocity and for possible directions (changing at Poisson times) is obtained by means of a suitable representation of the random motion in terms of independent, integrated telegraph signals.
Abstract: The exact joint distribution of the position of a particle performing a planar random motion with finite velocity and for possible directions (changing at Poisson times) is obtained This is carried out by means of a suitable representation of the random motion in terms of independent, integrated telegraph signals The singular component of the distribution is examined in detail and some asymptotic features of the results are investigated
39 citations
TL;DR: In this paper, the conditional Feynman-Kac functional is used to derive the Laplace transforms of conditional maximum distributions of processes related to third-and fourth-order equations.
37 citations
TL;DR: In this article, it is shown that the sojourn time of Brownian motion B(t), t>0 on the positive half-line, during the interval [0, t] and under the condition B (t)=0, is uniformly distributed, while it has the form of the corrected arc-sine law when the condition X(t)>0 is assumed.
Abstract: It is well known that the sojourn time of Brownian motion B(t), t>0 on the positive half-line, during the interval [0, t] and under the condition B(t)=0, is uniformly distributed, while it has the form of the “corrected arc-sine law” when the condition B(t)>0 is assumed We find the analogues of these laws for “processes” X(t), t>0 governed by signed measures whose densities are the fundamental solutions of third and fourth-order heat-type equations Surprisingly, both laws hold for the fourth-order “process” The uniform law is still valid for the third-order “process” but a different law emerges when the condition X(t)>0 is considered
28 citations
TL;DR: In this paper, the authors analyzed the asymptotic behavior of the rescaled solution to the linear Korteweg-de Vries equation when the initial conditions are supposed to be random and weakly dependent.
Abstract: We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.
17 citations
TL;DR: In this paper, the sojourn time of Brownian motion is shown to converge to the classical arc-sine law as u! 1 and becomes the uniform law asu = 1.
11 citations