Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_α$

Misiewicz Jolanta K.

GDML_Books, (1996), p.

Résumé

CONTENTSI. Introduction..........................................................................................................5II. Pseudo-isotropic random vectors........................................................................9  II.1. Symmetric stable vectors................................................................................9  II.2. Pseudo-isotropic random vectors..................................................................15  II.3. Elliptically contoured vectors..........................................................................23  II.4. α-symmetric random vectors..........................................................................27  II.5. Substable random vectors.............................................................................32III. Exchangeability and pseudo-isotropy.................................................................35  III.1. Pseudo-isotropic exchangeable sequences.................................................35  III.2. Schoenberg-type theorems..........................................................................40  III.3. Some generalizations...................................................................................43IV. Stable and substable stochastic processes.....................................................45  IV.1. Gaussian processes and Reproducing Kernel Hilbert Spaces....................45  IV.2. Elliptically contoured processes..................................................................47  IV.3. Symmetric stable stochastic processes......................................................50  IV.4. Spectral representation of symmetric stable processes.............................56  IV.5. Substable and pseudo-isotropic stochastic processes...............................59  IV.6. $L_α $-dependent stochastic integrals.......................................................62  IV.7. Random limit theorems...............................................................................63V. Infinite divisibility of substable stochastic processes..........................................64  V.1. Infinitely divisible distributions. Lévy measures............................................66  V.2. Approximative logarithm................................................................................68  V.3. Infinite divisibility of substable random vectors..............................................73  V.4. Infinite divisibility of substable processes......................................................77References...........................................................................................................80Index......................................................................................................................90

1991 Mathematics Subject Classification: Primary 46A15, 60B11; Secondary 60G07, 46B20, 60E07, 60K99.

Détail

Zbl 0948.46013

EUDML-ID : urn:eudml:doc:270064