Showing papers by "Enzo Orsingher published in 1999"

On the maximum of the generalized Brownian bridge

Abstract: We present some extensions of the distributions of the maximum of the Brownian bridge in [0,t] when the conditioning event is placed at a future timeu>t or at an intermediate timeu t andu

Iterated processes and their applications to higher order differential equations

Abstract: In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types. Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure. Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.

On the vector process obtained by iterated integration of the telegraph signal

Abstract: We analyse the vector process (X0(t);X1(t);:::;Xn(t), t > 0) where Xk(t) = t R 0 XkA1(s)ds, k = 1;:::;n, and X0(t) is the two-valued telegraph process. In particular, the hyperbolic equations governing the joint distri- butions of the process are derived and analysed. Special care is given to the case of the process (X0(t);X1(t); X2(t), t > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.