caa a22 4500 605519625 CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9392-1 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9392-1 Probability Law and Flow Function of Brownian Motion Driven by a Generalized Telegraph Process [Elektronische Daten] [Antonio Di Crescenzo, Shelemyahu Zacks] We consider a standard Brownian motion whose drift alternates randomly between a positive and a negative value, according to a generalized telegraph process. We first investigate the distribution of the occupation time, i.e. the fraction of time when the motion moves with positive drift. This allows to obtain explicitly the probability law and the flow function of the random motion. We discuss three special cases when the times separating consecutive drift changes have (i) exponential distribution with constant rates, (ii) Erlang distribution, and (iii) exponential distribution with linear rates. In conclusion, in view of an application in environmental sciences we evaluate the density of a Wiener process with infinitesimal moments alternating at inverse Gaussian distributed random times. Springer Science+Business Media New York, 2013 Standard Brownian motion nationallicence Alternating drift nationallicence Alternating counting process nationallicence Exponential random times nationallicence Erlang random times nationallicence Modified Bessel function nationallicence Two-index pseudo-Bessel function nationallicence Di Crescenzo Antonio Dipartimento di Matematica, Università di Salerno, 84084, Fisciano, SA, Italy aut Zacks Shelemyahu Department of Mathematical Sciences, Binghamton University, 13902-6000, Binghamton, NY, USA aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 761-780 1387-5841 17:3<761 2015 17 11009 https://doi.org/10.1007/s11009-013-9392-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9392-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Di Crescenzo Antonio Dipartimento di Matematica, Università di Salerno, 84084, Fisciano, SA, Italy aut NATIONALLICENCE 700 1- Zacks Shelemyahu Department of Mathematical Sciences, Binghamton University, 13902-6000, Binghamton, NY, USA aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 761-780 1387-5841 17:3<761 2015 17 11009