• Corpus ID: 231740570

Hypoelliptic entropy dissipation for stochastic differential equations

@inproceedings{Feng2021HypoellipticED,
  title={Hypoelliptic entropy dissipation for stochastic differential equations},
  author={Qi Feng and Wuchen Li},
  year={2021}
}
We study convergence behaviors of degenerate and non-reversible stochastic differential equations. Our method follows a Lyapunov method in probability density space, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We construct a weighted Fisher information induced Gamma calculus method with a structure condition. Under this condition, an explicit algebraic tensor is derived to guarantee the convergence rate for the probability density function… 

Figures from this paper

Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations
. We study long-time dynamical behaviors of weakly self-consistent Vlasov-Fokker-Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which characterizes the

References

SHOWING 1-10 OF 54 REFERENCES
Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equations.
We formulate explicit bounds to guarantee the exponential dissipation for some non-gradient stochastic differential equations towards their invariant distributions. Our method extends the connection
Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift
We investigate the existence of steady states and exponential decay for hypocoercive Fokker--Planck equations on the whole space with drift terms that are linear in the position variable. For this
Hypocoercivity of linear degenerately dissipative kinetic equations
In this paper we develop a general approach of studying the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the
Asymptotic Behavior of Thermal Nonequilibrium Steady States for a Driven Chain of Anharmonic Oscillators
Abstract: We consider a model of heat conduction introduced in [6], which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature
ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here
Ergodic properties of Markov processes
In these notes we discuss Markov processes, in particular stochastic differential equations (SDE) and develop some tools to analyze their long-time behavior. There are several ways to analyze such
Stochastic Hamiltonian Systems : Exponential Convergence to the Invariant Measure , and Discretization by the Implicit Euler Scheme
In this paper we carefully study the large time behaviour of u(t, x, y) := Ex,y f(Xt, Yt)− ∫ f dμ, where (Xt, Yt) is the solution of a stochastic Hamiltonian dissipative system with non gbally
Variational methods for the kinetic Fokker-Planck equation
We develop a functional analytic approach to the study of the Kramers and kinetic Fokker-Planck equations which parallels the classical $H^1$ theory of uniformly elliptic equations. In particular, we
Large-time behavior of non-symmetric Fokker-Planck type equations
Large time asymptotics of the solutions to non-symmetric Fokker- Planck type equations are studied by extending the entropy method to this case. We present a modified Bakry-Emery criterion that
...
...