We investigate the relativistic Brownian motion in the context of Fokker-Planck equation. Due to the multiplicative noise term of the corresponding relativistic Langevin equation many Fokker-Planck equations can be generated. Here, we only consider the Ito, Stratonovich and Hänggi-Klimontovich approaches. We analyze the behaviors of the second moment of momentum in terms of temperature. We show that the second moment increases with the temperature T for all three approaches. Also, we present differential equations for more complicated averages of the momentum. In a specific case, in the Ito approach, we can obtain an analytical solution of the temporal evolution of an average of the momentum. We present approximate solutions for the probability density for all three cases.

The generalized Bose-Einstein distribution, within the dilute gas assumption, in the nonextensive Tsallis statistics is worked without approximation for the Bose-Einstein condensation (BEC). The results obtained are compared with the recent results presented in Int. J. Mod. Phys. B 14, 405 (2000) by L. Salasnich. Furthermore, in order to promote a complete analysis for the BEC in the nonextensive scenario we also find exact expression within the normalized constraints in a harmonic trap.