Geodesic
The invariant and
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 135-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $\xi(t)$, $t\in[0,1]$ be a strictly stable process with the index of stability $\alpha\in(0,2)$. By $\mathcal P_\xi$ we denote the law of $\xi$ in the Skorokhod space $\mathbb D[0,1]$. For arbitrary strictly stable process $\xi$ we construct $\mathcal P_\xi-$quasi-invariant semigroup of transformations of $\mathbb D[0,1]$. For strictly stable processes with positive and negative jumps we construct $\mathcal P_\xi-$quasi-invariant group of transformations of $\mathbb D[0,1]$. In symmetric case this group is a group of the invariant transformations. 
@article{ZNSL_2006_339_a8,
     author = {N. V. Smorodina},
     title = {The invariant and},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--150},
     year = {2006},
     volume = {339},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a8/}
}
TY  - JOUR
AU  - N. V. Smorodina
TI  - The invariant and
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 135
EP  - 150
VL  - 339
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a8/
LA  - ru
ID  - ZNSL_2006_339_a8
ER  - 
%0 Journal Article
%A N. V. Smorodina
%T The invariant and
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 135-150
%V 339
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a8/
%G ru
%F ZNSL_2006_339_a8
N. V. Smorodina. The invariant and. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 135-150. http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a8/

[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, 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] V. Skorokhod, “O differentsiruemosti mer, sootvetstvuyuschikh sluchainym protsessam, I”, Teoriya veroyatn. i ee primen., 2 (1957), 629–649

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

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

[7] I. M. Gel'fand, M. I. Graev, A. M. Vershik, “Representations of the group of diffeomorphisms”, Russian Math. Surveys, 30 (1975), 3–50 | MR

[8] 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

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

[10] V. M. Zolotarev, Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983 | MR