Relativistic diffusion processes and random walk models

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  • 1 August 2006
Abstract
The non-relativistic standard model for a continuous, one-parameter diffusion process is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate at velocities larger than the speed of light. In this paper, relativistic non-Markovian generalizations of the Wiener process are constructed from (i) a simple random walk model and (ii) by pursuing an axiomatic approach. The relativistic transition PDFs obtained this way avoid superluminal propagation speeds, but still depend on a single diffusion parameter only (e.g., in contrast to the two-parameter solutions of the telegraph equation).

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