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Limiting distributions of randomly accelerated motions. (English) Zbl 0927.60033
Lith. Math. J. 37, No. 3, 219-229 (1997) and Liet. Mat. Rink. 37, No. 3, 295-308 (1997).
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.
##### MSC:
 60F05 Central limit and other weak theorems 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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