Central limit theorem for a class of relativistic diffusions

Abstract

Two similar Minkowskian diffusions have been considered, on one hand by Debbasch and co-workers [J. Math. Phys. 40, 2891 (2001); Eur. Phys. J. 19, 37 (2001); 23, 487 (2001); J. Stat. Phys. 88, 945 (1997); 90, 1179 (1998)], and on the other hand by Dunkel and Hänggi [Phys. Rev. E 71, 016124 (2005); 72, 036106 (2005)]. We address here two questions, asked by Debbasch and Rivet [J. Stat. Phys. 90, 1179 (1998)] and by Dunkel and Hänggi [Phys. Rev. E 71, 016124 (2005); 72, 036106 (2005)], respectively, about the asymptotic behavior 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 by Dunkel and Hänggi [Phys. Rev. E 71, 016124 (2005)]. © 2007 American Institute of Physics.