A stochastic approach to relativistic diffusions
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Mon, 11/05/2009 15:45 |
Dr Ismael Bailleul (Cambridge) |
Stochastic Analysis Seminar  |
Oxford-Man Institute |
| A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced by C. Chevalier and F Debbasch, both in a heuristic and analytic way. Roughly speaking, they are characterised by the existence at each (proper) time (of the moving particle) of a (local) rest frame where the random part of the acceleration of the particle (computed using the time of the rest frame) is brownian in any spacelike direction of the frame. I will explain how the tools of stochastic calculus enable us to give a concise and elegant description of these random paths on any Lorentzian manifiold. A mathematically clear definition of the the one-particle distribution function of the dynamics will emerge from this definition, and whose main property will be explained. This will enable me to obtain a general H-theorem and to shed some light on links between probablistic notions and the large scale structure of the manifold. All necessary tools from stochastic calculus and geometry will be explained. | |||