Wasserstein metric convergence method for Fokker–Planck equations with point controls
نویسندگان
چکیده
منابع مشابه
Wasserstein metric convergence method for Fokker-Planck equations with point controls
In this work we present a result on linear diffusion equations with point controls. This is the first partial result obtained along the completion of [5] which includes more general nonlinear diffusion equations. The main focus here is showing how recent variational principles based on Wasserstein metric, used to solve homogeneous diffusion equations, can actually be extended to solving nonhomo...
متن کاملConvergence in the Wasserstein Metric for MarkovChain
This paper gives precise bounds on the convergence time of the Gibbs sampler used in the Bayesian restoration of a degraded image. Convergence to stationarity is assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergen...
متن کاملConvergence to equilibrium in Wasserstein distance for Fokker-Planck equations
We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and co...
متن کاملConvergence of the Population Dynamics algorithm in the Wasserstein metric
We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the special endogenous solution to a stochastic fixed-point equation of the form: R D = Φ(Q,N, {Ci}, {Ri}), where (Q,N, {Ci}) is a real-valued random vector with N ∈ N, and {Ri}i∈N is a sequence of i.i.d. copies of R, independent ...
متن کاملApproximation of parabolic equations using the Wasserstein metric
We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial diflerential équations. One remarkable feature of the algorithms presented hère is that derivatives do not enter into the variational principleSj so, for example, discontinuous approximations may be used for approximating the h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.10.003