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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 339, Pages 135–150
(Mi znsl162)
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This article is cited in 4 scientific papers (total in 4 papers)
The invariant and
quasi-invariant transformations of the stable processes
with independent increments
N. V. Smorodina Saint-Petersburg State University
Abstract:
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.
Received: 11.11.2006
Citation:
N. V. Smorodina, “The invariant and
quasi-invariant transformations of the stable processes
with independent increments”, Probability and statistics. Part 10, Zap. Nauchn. Sem. POMI, 339, POMI, St. Petersburg, 2006, 135–150; J. Math. Sci. (N. Y.), 145:2 (2007), 4914–4922
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https://www.mathnet.ru/eng/znsl162 https://www.mathnet.ru/eng/znsl/v339/p135
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Abstract page: | 206 | Full-text PDF : | 55 | References: | 48 |
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