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A stochastic approach to relativistic diffusions. (English) Zbl 1206.60053

The purpose of the author is threefold: – first, to unify the presentation of a relativistic diffusions introduced separately by probabilistics (Dudley, Franchie-Le Jan, Angst-Franchi) and by theoretical physicists (Debbasch and al.); – second, to exhibit a “one particle distribution function”, density of the harmonic measure of a Cauchy hypersurface, and to establish a non-trivial theorem stating that this function is co-harmonic; – third, to prove an infinitesimal version of a “\(H\)-theorem”, which states that under natural assumptions, the entropy cannot decrease, in the relativistic setting too, in accordance with the analogous property of classical (Boltzmann) statistical mechanics.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
83C99 General relativity
58J65 Diffusion processes and stochastic analysis on manifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C10 Equations of motion in general relativity and gravitational theory
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