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PreprintCC BY-NC-SA 4.0HAL

Stable invariant measures in linear dynamics

  • Valentin Gillet
Open at sourcePDFCite

Abstract

We study the existence of stable invariant measures for operators and strongly continuous semigroups of operators on Banach spaces admitting either a dense bilateral backward orbit or a sufficiently rich family of eigenvectors. These invariant measures are realized as the distributions of stochastic integrals with respect to stable random measures. We also discuss invariant measures with other classes of distributions for such operators and semigroups.

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Cite

BibTeXRIS
BibTeX
@misc{gillet2026stable,
  title = {{Stable invariant measures in linear dynamics}},
  author = {Valentin Gillet},
  howpublished = {HAL},
  year = {2026},
  month = jun,
  url = {https://hal.science/hal-05789641v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Stable invariant measures in linear dynamics
AU  - Valentin Gillet
PY  - 2026
DA  - 2026/06/29
PB  - HAL
UR  - https://hal.science/hal-05789641v1
AB  - We study the existence of stable invariant measures for operators and strongly continuous semigroups of operators on Banach spaces admitting either a dense bilateral backward orbit or a sufficiently rich family of eigenvectors. These invariant measures are realized as the distributions of stochastic integrals with respect to stable random measures. We also discuss invariant measures with other classes of distributions for such operators and semigroups.
ER  -