Central Limit Theorem for a Class of Relativistic Diffusions

Details Central Limit Theorem for a Class of Relativistic Diffusions Central Limit Theorem for a Class of Relativistic Diffusions

2007-02-16

arxiv.org/abs/math/0702481v2

Mathematics

Probability

20 pages

Scientific paper

10.1063/1.2759441

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for a class of Minkowskian diffusions, to which the two above ones belong. As a consequence, we correct a partially wrong guess in [DH1].

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