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.
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Additional information
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.
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Conti, P.L., Orsingher, E. Limiting distributions of randomly accelerated motions. Lith Math J 37, 219–229 (1997). https://doi.org/10.1007/BF02465352
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DOI: https://doi.org/10.1007/BF02465352