Sharp Harnack inequalities for a family of hypoelliptic diffusions
نویسندگان
چکیده
منابع مشابه
Harnack Inequalities for Degenerate Diffusions
We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators [8, 9, 6]. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scaleinvariant Harnack inequality fo...
متن کاملPeriodic Homogenization for Hypoelliptic Diffusions
Abstract We study the long time behavior of an Ornstein–Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation. We also derive upper bounds on the convergence rate in several ...
متن کاملHarnack inequalities and Gaussian estimates for a class of hypoelliptic operators
We announce some results obtained in a recent study [14], concerning a general class of hypoelliptic evolution operators in R. A Gaussian lower bound for the fundamental solution and a global Harnack inequality are given.
متن کاملSampling Conditioned Hypoelliptic Diffusions
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this metho...
متن کاملSmoothness of Harmonic Maps for Hypoelliptic Diffusions
Harmonic maps are viewed as maps sending a xed diiusion to manifold-valued martingales. Under a convexity condition, we prove that the continuity of real-valued harmonic functions implies the continuity of harmonic maps. Then we prove with a probabilistic method that continuous harmonic maps are smooth under HH ormander's condition; the proof relies on the study of martingales with values in th...
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: Journal of Mathematical Physics
سال: 2017
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4977475