Uniform exponential ergodicity of stochastic dissipative systems

Beniamin Goldys; Bohdan Maslowski

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 4, page 745-762
  • ISSN: 0011-4642

Abstract

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We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in ℝ d with d ≤ 3 .

How to cite

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Goldys, Beniamin, and Maslowski, Bohdan. "Uniform exponential ergodicity of stochastic dissipative systems." Czechoslovak Mathematical Journal 51.4 (2001): 745-762. <http://eudml.org/doc/30669>.

@article{Goldys2001,
abstract = {We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in $\mathbb \{R\}^d$ with $d\le 3$.},
author = {Goldys, Beniamin, Maslowski, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {dissipative system; compact semigroup; exponential ergodicity; spectral gap; dissipative system; compact semigroup; exponential ergodicity; spectral gap},
language = {eng},
number = {4},
pages = {745-762},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniform exponential ergodicity of stochastic dissipative systems},
url = {http://eudml.org/doc/30669},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Goldys, Beniamin
AU - Maslowski, Bohdan
TI - Uniform exponential ergodicity of stochastic dissipative systems
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 745
EP - 762
AB - We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in $\mathbb {R}^d$ with $d\le 3$.
LA - eng
KW - dissipative system; compact semigroup; exponential ergodicity; spectral gap; dissipative system; compact semigroup; exponential ergodicity; spectral gap
UR - http://eudml.org/doc/30669
ER -

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