an:01151886
Zbl 0927.60033
Conti, P. L.; Orsingher, E.
Limiting distributions of randomly accelerated motions
EN
Lith. Math. J. 37, No. 3, 219-229 (1997) and Liet. Mat. Rink. 37, No. 3, 295-308 (1997).
00046413
1997
j
60F05 60J20
order statistics; central limit theorem; uniform acceleration; Poisson process
Summary: 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 of \(X(t)\) (suitably normalized), conditionally on the number \(n\) of changes of acceleration, tends in distribution to a normal variate as \(n\) goes to infinity. The asymptotic normality of the unconditional distribution of \(X(t)\) for large values of \(t\) is also shown. The study of these limiting distributions is motivated by the difficulty of evaluating exactly the conditional and unconditional probability laws of \(X(t)\). In fact, the results obtained permit us to give useful approximations of the probability distributions of the position of the particle.