Free Brownian motion of relativistic particles

The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are explicitly found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal corrections, to the both relaxation times T (of stationary autocorrelations) and transient relaxation time of momentum, appear slowing down the processes. The transient relaxation time of the velocity does not depend explicitly on temperature, T(v0)=m(v0)/γ≡ɛ0/γc2, and it is proportional to the initial energy of a relativistic Brownian particle.