Ellipticity and Ergodicity

نویسندگان

  • DEREK W. ROBINSON
  • ADAM SIKORA
چکیده

Let S = {St}t≥0 be the submarkovian semigroup on L2(R ) generated by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients cij . Further let Ω be an open subset of R . We prove that S leaves L2(Ω) invariant if, and only if, it is invariant under the flows generated by the vector fields Yi = ∑d j=1 cij∂j .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exponential Ergodicity and Raleigh-schrödinger Series for Infinite Dimensional Diffusions

, with η ∈ T d , where the coefficients ai, bi are finite range, bounded with bounded second order partial derivatives and the ellipticity assumption infi,η ai(η) > 0 is satisfied. We prove that whenever ν is an invariant measure for this diffusion satisfying the logarithmic Sobolev inequality, then the dynamics is exponentially ergodic in the uniform norm, and hence ν is the unique invariant m...

متن کامل

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

متن کامل

Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in Z , d ≥ 2. We first prove an invariance principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for ran...

متن کامل

Stochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environment

We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient), we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends p...

متن کامل

Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control

For a class of Bellman equations in bounded domains we prove that suband supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a condition involving also the drift is further imposed. We apply this result to stochastic control problems, in particular to an exit problem and to the small di...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009