Decompositions of stochastic processes based on irreductible group representations

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dc.creatorPeccati, Giovanni
dc.creatorPycke, Jean-Renaud
dc.date2005-09-23
dc.date.accessioned2026-07-07T06:18:52Z
dc.date.available2026-07-07T06:18:52Z
dc.descriptionLet G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible representations of G. In the particular case of a Gaussian process with a G-invariant law, such a decomposition gives a very general explanation of a classic identity in law - between quadratic functionals of a Brownian bridge - due to Watson (1961). Several relations with Karhunen-Loève expansions are discussed, and some applications and extensions are given - in particular related to Gaussian processes indexed by a torus.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0509569
dc.identifierhttp://arxiv.org/abs/math/0509569
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94882
dc.subjectProbability
dc.subjectMCS: 60G15 60G07 60H05 20C15
dc.titleDecompositions of stochastic processes based on irreductible group representations
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