Geodesic
The measure preserving transformations of the multidimensional stable Lévy processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 242-252 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\xi(t)$, $t\in[0,1]$ be a $\alpha-$stable Lévy process in $\mathbb R^d$. Denote by $\mathcal P_\xi$ the measure generated by $\xi$ in Skorokhod space $\mathbb D([0,1],\mathbb R^d)$. Under some conditions on the spectral measure of the process $\xi$ we construct a group of the $\mathcal P_\xi-$preserving transformations of $\mathbb D([0,1]\mathbb R^d$. 
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N. V. Smorodina. The measure preserving transformations of the multidimensional stable Lévy processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 242-252. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a13/

[1] Y. Takahashi, “Absolute continuity of Poisson random fields”, Publ. Res. Inst. Math. Sci., 26 (1990), 629–649 | DOI | MR

[2] J. Kerstan, K. Mattes, and J. Mecke, Infinite divisible point processes, Akademie-Verlag, Berlin, 1978

[3] W. Linde, Infinitely divisible and stable measures on Banach spaces, Teubner, Leipzig, 1983 | MR | Zbl

[4] A. V. Skorokhod, “O differentsiruemosti mer, sootvetstvuyuschikh sluchainym protsessam. I”, Teoriya Veroyatn. i ee primen., II (1957), 629–649

[5] A. V. Skorokhod, Issledovaniya po teorii sluchainykh protsessov, Izd-vo Kievskogo un-ta, 1961

[6] A. V. Skorokhod, Stokhasticheskie protsessy s nezavisimymi prirascheniyami, Nauka, M., 1986 | MR

[7] N. V .Smorodina, “Invariantnye i kvaziinvariantnye preobrazovaniya mer, otvechayuschikh ustoichivym protsessam s nezavisimymi prirascheniyami”, Zap. nauchn. semin. POMI, 339, 2006, 135–150 | MR | Zbl

[8] J .F. C. Kingman, Poisson Processes, Oxford, 1993 | MR | Zbl

[9] A. G. Kurosh, Teoriya grupp, Gostekhizdat, Moskva, 1953 | MR

[10] I. M. Gel'fand, M. I. Graev, A. M. Vershik, “Representations of the group of diffeomorphisms”, Uspehi Mat. Nauk, 30:6 (1975), 3–50 | MR | Zbl

[11] A. Vershik, N. Tsilevich, “Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures”, C. R. Acad. Sci. Paris Ser. I Math., 329 (1999), 163–168 | MR | Zbl

[12] P. Billingsli, Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR