Diagonalization of the Lévy Laplacian and related stable processes

Hui Hsiung Kuo, Nobuaki Obata, Kimiaki Saitô

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

Eigenfunctions of the Lévy Laplacian with an arbitrary real number as an eigenvalue are constructed by means of a coordinate change of white noise distributions. The Lévy Laplacian is diagonalized on the direct integral Hilbert space of such eigenfunctions and the corresponding equi-continuous semigroup is obtained. Moreover, an infinite dimensional stochastic process related to the Lévy Laplacian is constructed from a one-dimensional stable process.

Original languageEnglish
Pages (from-to)317-331
Number of pages15
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume5
Issue number3
DOIs
Publication statusPublished - 2002 Sep

Keywords

  • Diagonalization
  • Equi-continuous semigroup
  • Exponential coordinate change
  • Gaussian space
  • Gel'fand triple
  • Lévy Laplacian
  • S-transform
  • Self-adjoint extension
  • Stable processes
  • Wiener-Itô decomposition

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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