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…
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Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations
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. 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.
- Mathematics
- 2020
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…
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré
- Mathematics
- 2007
Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift
- Mathematics
- 2014
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
- Mathematics
- 2009
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
- Mathematics
- 2000
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
- Mathematics
- 2001
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
- Mathematics
- 2006
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
- Mathematics
- 2002
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
- Mathematics
- 2019
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
- Mathematics
- 2008
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…