The method of stochastic characteristics for linear second-order hypoelliptic equations

DOI10.1214/22-PS11MaRDI QIDQ2683171

Juraj Földes, David P. Herzog

Publication date: 3 February 2023

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

Full work available at URL: https://arxiv.org/abs/2112.06404

zbMATH Keywords

stochastic characteristicshypoelliptic operatorboundary-valued PDE

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Green's functions for ordinary differential equations (34B27) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Hypoelliptic equations (35H10) Boundary value problems for linear higher-order PDEs (35G15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Harnack inequality for hypoelliptic second order partial differential operators
• The transition from ergodic to explosive behavior in a family of stochastic differential equations
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
• Wiener-type tests from a two-sided Gaussian bound
• Recurrence and invariant measures for degenerate diffusions
• Ergodic properties of a model for turbulent dispersion of inertial particles
• On the Dirichlet problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion
• Ergodic property of recurrent diffusion processes
• Lower bounds for densities of Asian type stochastic differential equations
• Wiener criterion for a class of degenerate elliptic operators
• The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. I
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Dirichlet problem for some hypoelliptic operators
• Local asymptotic classes for the successive primitives of Brownian motion
• Tube estimates for diffusion processes under a weak Hörmander condition
• Non-equilibrium steady states for networks of oscillators
• Stochastic dynamics out of equilibrium. Lecture notes from the IHP trimester, Institut Henri Poincaré (IHP), Paris, France, April -- July, 2017
• Ergodicity of the finite-dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise
• A noise-induced transition in the Lorenz system
• Density estimates and short-time asymptotics for a hypoelliptic diffusion process
• A functional law of the iterated logarithm for weakly hypoelliptic diffusions at time zero
• Sharp estimates for Geman-Yor processes and applications to arithmetic average Asian options
• Couplings and quantitative contraction rates for Langevin dynamics
• T. E. Harris's contributions to recurrent Markov processes and stochastic flows
• Hypoelliptic second order differential equations
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• An invariant Harnack inequality for a class of hypoelliptic ultraparabolic equations
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution to the Cauchy Problem for Parabolic Equations
• Clustering and collisions of heavy particles in random smooth flows
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Markov Chains and Stochastic Stability
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Ergodicity for the Navier‐Stokes equation with degenerate random forcing: Finite‐dimensional approximation
• Weighted L ²-contractivity of Langevin dynamics with singular potentials
• Sensitivity of steady states in a degenerately damped stochastic Lorenz system
• Hypocoercivity Properties of Adaptive Langevin Dynamics
• Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials
• Mutual Absolute Continuity of Harmonic and Surface Measures for Hormander Type Operators