A stochastic approach to relativistic diffusions

DOI10.1214/09-AIHP341zbMath1206.60053arXiv0810.5662MaRDI QIDQ1958514

Ismaël Bailleul

Publication date: 4 October 2010

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/0810.5662

zbMATH Keywords

harmonic measuregeneral relativitydiffusionsharmonic functions\(H\)-theorem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) General relativity (83C99) Diffusion processes and stochastic analysis on manifolds (58J65) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Equations of motion in general relativity and gravitational theory (83C10)

Related Items

Homogenization of dissipative, noisy, Hamiltonian dynamics ⋮ Random dynamical systems, rough paths and rough flows ⋮ Random motion of light-speed particles ⋮ Brownian motion at the speed of light: a new Lorentz invariant family of processes ⋮ Homogenisation for anisotropic kinetic random motions ⋮ A Poincaré cone condition in the Poincaré group ⋮ From Riemannian to Relativistic Diffusions ⋮ Curvature diffusions in general relativity ⋮ Hypocoercivity for Kolmogorov backward evolution equations and applications ⋮ Solutions of hyperbolic stochastic PDEs on bounded and unbounded domains ⋮ Phase space homogenization of noisy Hamiltonian systems ⋮ Small mass limit of a Langevin equation on a manifold ⋮ Nonexplosion criteria for relativistic diffusions ⋮ Entropy anomaly in Langevin-Kramers dynamics with a temperature gradient, matrix drag, and magnetic field ⋮ On the Poisson boundary of the relativistic Brownian motion ⋮ Trends to equilibrium for a class of relativistic diffusions ⋮ A probabilistic view on singularities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame
• Covariant Kolmogorov equation and entropy current for the relativistic Ornstein-Uhlenbeck process
• The Dirichlet problem at infinity for manifolds of negative curvature
• Relativistic diffusion in Gödel's universe
• Relativistic Ornstein-Uhlenbeck process
• A new approach to the Martin boundary via diffusions conditioned to hit a compact set
• Poisson boundary of a relativistic diffusion
• Lorentz-invariant Markov processes in relativistic phase space
• Where does randomness lead in spacetime?
• Relativistic diffusions and Schwarzschild geometry
• An H-theorem for the general relativistic Ornstein-Uhlenbeck process
• A UNIFYING APPROACH TO RELATIVISTIC DIFFUSIONS AND H-THEOREMS
• Central limit theorem for a class of relativistic diffusions
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• The singularities of gravitational collapse and cosmology
• A diffusion process in curved space–time
• Elements of Information Theory
• Relativistic diffusions: A unifying approach
• Minimal Positive Harmonic Functions
• Relativistic fluid dynamics: physics for many different scales
• Invariance of the relativistic one-particle distribution function

This page was built for publication: A stochastic approach to relativistic diffusions