Where does randomness lead in spacetime?
ESAIM: Probability and Statistics (2010)
- Volume: 14, page 16-52
- ISSN: 1292-8100
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topBailleul, Ismael, and Raugi, Albert. "Where does randomness lead in spacetime?." ESAIM: Probability and Statistics 14 (2010): 16-52. <http://eudml.org/doc/250841>.
@article{Bailleul2010,
abstract = {
We provide an alternative algebraic and geometric approach to the results of [I. Bailleul, Probab. Theory Related Fields141 (2008) 283–329] describing the asymptotic behaviour of the relativistic diffusion.
},
author = {Bailleul, Ismael, Raugi, Albert},
journal = {ESAIM: Probability and Statistics},
keywords = {Random walks on groups; Poisson boundary; special relativity; causal boundary.; relativistic diffusion; invariant sigma algebra; asymptotic behavior},
language = {eng},
month = {2},
pages = {16-52},
publisher = {EDP Sciences},
title = {Where does randomness lead in spacetime?},
url = {http://eudml.org/doc/250841},
volume = {14},
year = {2010},
}
TY - JOUR
AU - Bailleul, Ismael
AU - Raugi, Albert
TI - Where does randomness lead in spacetime?
JO - ESAIM: Probability and Statistics
DA - 2010/2//
PB - EDP Sciences
VL - 14
SP - 16
EP - 52
AB -
We provide an alternative algebraic and geometric approach to the results of [I. Bailleul, Probab. Theory Related Fields141 (2008) 283–329] describing the asymptotic behaviour of the relativistic diffusion.
LA - eng
KW - Random walks on groups; Poisson boundary; special relativity; causal boundary.; relativistic diffusion; invariant sigma algebra; asymptotic behavior
UR - http://eudml.org/doc/250841
ER -
References
top- A. Ancona, Théorie du potentiel sur les graphes et les variétés. École d'été de Probabilités de Saint-Flour XVIII, 1988. Lect. Notes Math.1427 (1990) 1–112. Springer, Berlin.
- D. Applebaum, Compound Poisson processes and Lévy processes in groups and symmetric spaces. J. Theoret. Probab.13 (2000) 383–425.
- D. Applebaum and H. Kunita, Lévy flows on manifolds and Lévy processes on Lie groups. J. Math. Kyoto Univ.33 (1993) 1103–1123.
- I. Bailleul, Poisson boundary of a relativistic diffusion. Probab. Theory Related Fields141 (2008) 283–329.
- P. Baldi and M. Chaleyat-Maurel, Sur l'équivalent du module de continuité des processus de diffusion, in Séminaire de Probabilités, XXI. Lect. Notes Math.1247 (1987) 404–427. Springer, Berlin.
- J.K. Beem, P.E. Ehrlich and K.L. Easley, Global Lorentzian geometry, volume 202 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, second edition (1996).
- A.N. Borodin and P. Salminen, Handbook of Brownian motion – facts and formulae. Probability and its Applications. Birkhäuser Verlag, Basel. Second edition (2002).
- Y. Derriennic, Lois “zéro ou deux” pour les processus de Markov. Applications aux marches aléatoires. Ann. Inst. H. Poincaré Sect. B (N.S.)12 (1976) 111–129.
- R.M. Dudley, Lorentz-invariant Markov processes in relativistic phase space. Ark. Mat.6 (1966) 241–268.
- R.M. Dudley, Asymptotics of some relativistic Markov processes. Proc. Natl. Acad. Sci. USA70 (1973) 3551–3555.
- C. Frances, Géométrie et dynamique Lorentzienne conformes. École Normale Supérieure de Lyon (2002).
- R. Geroch, E.H. Kronheimer, and Roger Penrose, Ideal points in space-time. Proc. Roy. Soc. Lond. Ser. A327 (1972) 545–567.
- A. Grigor'yan, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Bull. Amer. Math. Soc. (N.S.)36 (1999) 135–249.
- Y. Guivarc'h. Une loi des grands nombres pour les groupes de Lie. In Séminaire de Probabilités, I . Exposé No. 8. Dépt. Math. Informat., Univ. Rennes, France (1976).
- T.R. Hurd, The projective geometry of simple cosmological models. Proc. Roy. Soc. Lond. Ser. A397 (1985) 233–243.
- N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North-Holland Mathematical Library, Vol. 24. North-Holland Publishing Co., Amsterdam, second edition (1989).
- F.I. Karpelevič, V.N. Tutubalin and M.G. Šur, Limit theorems for compositions of distributions in the Lobačevskiĭ plane and space. Teor. Veroyatnost. i Primenen.4 (1959) 432–436.
- M. Liao, Lévy processes in Lie groups, volume 162 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2004).
- J. Neveu, Mathematical foundations of the calculus of probability. Translated by Amiel Feinstein. Holden-Day Inc., San Francisco, Californie (1965).
- B. O'Neill, Semi-Riemannian geometry. With applications to relativity, volume 103 of Pure Appl. Math. Academic Press Inc. (Harcourt Brace Jovanovich Publishers), New York (1983).
- R.G. Pinsky, Positive harmonic functions and diffusion, volume 45 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1995).
- J.-J. Prat, Étude asymptotique et convergence angulaire du mouvement brownien sur une variété à courbure négative. C. R. Acad. Sci. Paris Sér. A-B280 Aiii (1975) A1539–A1542.
- A. Raugi, Fonctions harmoniques sur les groupes localement compacts à base dénombrable. Bull. Soc. Math. France, Mémoire54 (1977) 5–118.
- A. Raugi, Périodes des fonctions harmoniques bornées. In Seminar on Probability, Rennes, 1978 (French). Exposé No. 10. Univ. Rennes, France (1978).
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