Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes

DOI10.1214/14-PS249zbMath1323.60104arXiv1411.2752MaRDI QIDQ491376

David Applebaum

Publication date: 25 August 2015

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.2752

zbMATH Keywords

branching processesLévy processesstochastic partial differential equationsinvariant measureMehler semigroupOrnstein-Uhlenbeck processesoperator self-decomposabilityUrbanik semigroupcylindrical processskew-convolution semigroup

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (12)

Cointegration in continuous time for factor models ⋮ Invariant measures and boundedness in the mean for stochastic equations driven by Lévy noise ⋮ Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes ⋮ Time regularity for generalized Mehler semigroups ⋮ Ornstein-Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility ⋮ The cutoff phenomenon for the stochastic heat and wave equation subject to small Lévy noise ⋮ Functional inequalities for some generalised Mehler semigroups ⋮ The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise ⋮ The Heston stochastic volatility model in Hilbert space ⋮ On a class of stochastic partial differential equations with multiple invariant measures ⋮ Reflection positivity, duality, and spectral theory ⋮ Spontaneous Wave Formation in Stochastic Self-Driven Particle Systems

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