Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise

DOI10.1214/18-AIHP919zbMath1466.60046arXiv1707.01958OpenAlexW2976949979MaRDI QIDQ2337826

Ilya Pavlyukevitch, Alexei M. Kulik

Publication date: 20 November 2019

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01958

zbMATH Keywords

Lyapunov functionLangevin equationLévy processstable Lévy processBlumenthal-Getoor indexsingular driftnon-linear frictionergodic Markov processHölder-continuous drift

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Random vibrations in mechanics of particles and systems (70L05) Problems involving a system of particles with friction (70F40)

Related Items (4)

On ergodic properties of some Lévy-type processes ⋮ Moment bounds for dissipative semimartingales with heavy jumps ⋮ On regularization by a small noise of multidimensional odes with non-Lipschitz coefficients ⋮ Generalized Peano problem with Lévy noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Noise and vibration in friction systems
• Gaussian asymptotics for a non-linear Langevin type equation driven by an \(\alpha\)-stable Lévy noise
• Lévy flights in a steep potential well
• Sliding friction. Physical principles and applications.
• Singular stochastic differential equations.
• Theory of stochastic differential equations with jumps and applications.
• Perturbation of drift-type for Levy processes
• Ergodic behavior of Markov processes. With applications to limit theorems
• Small noise asymptotics and first passage times of integrated Ornstein-Uhlenbeck processes driven by \(\alpha\)-stable Lévy processes
• Diffusion coefficient of a Brownian particle with a friction function given by a power law
• Langevin equation with Coulomb friction
• Brownian motion with dry friction
• Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions.
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Brownian motion with dry friction: Fokker–Planck approach
• Contact Mechanics and Friction
• Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
• Non-Gaussian Velocity Distribution Function in a Vibrating Granular Bed
• Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models
• Some perturbations of drift-type for symmetric stable processes

This page was built for publication: Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise