Some properties of invariant measures of non symmetric dissipative stochastic systems
Some properties of invariant measures of non symmetric dissipative stochastic systems
复制标题
非对称耗散随机系统不变测度的一些性质
DOI：
10.1007/s004400100188
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发表时间：
2002
影响因子：
2
通讯作者：
B. Goldys
中科院分区：
文献类型：
--
作者：
G. Da Prato;A. Debussche;B. Goldys
摘要：我们考虑由具有耗散非线性项的随机偏微分方程生成的转移半群。 证明了不变测度的一个分部积分公式和一个对数Sobolev不等式。没有对称性或可逆性的假设。进一步证明了转移半群和基于不变测度的Sobolev空间嵌入的一些紧性结果。我们利用这些结果得到一个随机反应扩散方程的渐近性质。
Abstract. We consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms. We prove an integration by part formula and a Logarithmic Sobolev inequality for the invariant measure. No symmetry or reversibility assumptions are made. Furthemore we prove some compactness results on the transition semigroup and on the embedding of the Sobolev spaces based on the invariant measure. We use these results to derive asymptotic properties for a stochastic reaction–diffusion equation.