Continuity properties and infinite divisibility of stationary distributions of some generalized Ornstein-Uhlenbeck processes

DOI10.1214/08-AOP402zbMath1173.60007arXiv0804.4258OpenAlexW3102251138MaRDI QIDQ1011157

Ken-iti Sato, Alexander M. Lindner

Publication date: 8 April 2009

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.4258

zbMATH Keywords

Lévy processinfinite divisibilitygeneralized Ornstein-Uhlenbeck processdecomposable distributionPeres-Solomyak (P.S.) numberPisot-Vijayaraghavan (P.V.) numbersymmetrization of distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Stationary stochastic processes (60G10) Continuity and singularity of induced measures (60G30)

Related Items (13)

Selfdecomposability and semi-selfdecomposability in subordination of cone-parameter convolution semigroups ⋮ Ergodic properties of generalized Ornstein-Uhlenbeck processes ⋮ Distributions of exponential integrals of independent increment processes related to generalized gamma convolutions ⋮ Stationary solutions of the stochastic differential equation \(dV_t = V_t -dU_t + dL_t\) with Lévy noise ⋮ Weak Stationarity of Ornstein-Uhlenbeck Processes with Stochastic Speed of Mean Reversion ⋮ A quasi-infinitely divisible characteristic function and its exponentiation ⋮ Behaviors of multivariable finite Euler products in probabilistic view ⋮ Continuity properties and the support of killed exponential functionals ⋮ On exponential functionals of Lévy processes ⋮ Asymptotic properties of Fourier transforms of \(b\)-decomposable distributions ⋮ Asian options and meromorphic Lévy processes ⋮ A new formula for some linear stochastic equations with applications ⋮ Properties of stationary distributions of a sequence of generalized Ornstein-Uhlenbeck processes

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