| 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.
Dipartmento di Statistica, Probabilità Statistiche Applicate University of Rome “La Sapienza,” Italy. Published in Lietuvos
Matematikos Rinkinys, Vol. 37, No. 3, pp. 295–308, July–September, 1997. |
