We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space ℝ^d driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted L²-space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.

中文翻译：

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具有加性齐性噪声的随机反应扩散方程的吸引子

我们研究中的整个空间ℝ反应-扩散方程的解的渐近行为^d通过用有限的频谱量度的空间均匀的维纳过程驱动。建立了随机吸引子的存在，用于初始数据在任何维度上的合适加权L ^2-空间中，这是对PW Bates，K。Lu和B. Wang（2013）的结果的补充。使用短轨迹方法的元素可获得渐近紧致度。