Karhunen–Loève decomposition of Gaussian measures on Banach spaces
| Autor: | Jean-Charles Croix, Xavier Bay |
|---|---|
| Přispěvatelé: | École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne (UCA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Discrete mathematics Unbounded operator Pure mathematics orthogonal decomposition Eberlein–Šmulian theorem Banach manifold Finite-rank operator [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Compact operator on Hilbert space [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Gaussian measure Fréchet space Interpolation space MSC 60B11 60B12 28C20 Lp space or- thogonal decomposition Mathematics - Probability covariance operator Mathematics |
| Zdroj: | Probability and Mathematical Statistics Probability and Mathematical Statistics, 2019, 39 (2), pp.279-297. ⟨10.19195/0208-4147.39.2.3⟩ |
| DOI: | 10.19195/0208-4147.39.2.3⟩ |
| Popis: | International audience; The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the so-called Karhunen–Loève expansion. In this paper, we extend this result to Gaussian measures on Banach spaces in a very similar and constructive manner. In some sense, this can also be seen as a generalization of the spectral theorem for covariance operators associated with Gaussian measures on Banach spaces. In the special case of the standard Wiener measure, this decomposition matches with Lévy–Ciesielski construction of Brownian motion. |
| Databáze: | OpenAIRE |
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