Relativistic generalization of Brownian Motion

Relativistic Brownian Motion

Over the past one hundred years Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Initially proposed as a phenomenological paradigm for atomistic matter interactions, the original theory has ever since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics....

Relativistic Stochastic Processes

We review all recent contributions to the literature on stochastic processes. In particular, the Relativistic OrnsteinUhlenbeck Process is presented in detail, as is the intrinsic Brownian motion studied by Franchi and Le Jan. The Relativistic Brownian Motion of Dunkel and Hänggi is also reviewed, together with a model introduced by Oron and Horwitz. We finally suggest some possible future deve...

One-dimensional nonrelativistic and relativistic Brownian motions: A microscopic collision model

We study a simple microscopic model for the one-dimensional stochastic motion of a (non)relativistic Brownian particle, embedded into a heat bath consisting of (non)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic cons...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Relativistic Brownian Motion

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1 + 1 and 3 + 1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant d'Alembert form. Treating the spacelike and timelike fluctuations separately, we show that it is essential to take into account the analytic continuation of " un...