ON THE SPECTRAL SLLN AND POINTWISE ERGODIC THEOREM IN L(ALPHA)

• 成果类型: Article
• 署名作者: HOUDRE, C
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989527
• 发表日期: 1992
• 页码: 1731-1753
• 关键词: stochastic-processes; large numbers; STRONG LAW; fourier

摘要

We obtain criteria for the SLLN to hold for processes which are Fourier transforms of random measures. With this spectral approach, we also give criteria for the pointwise ergodic theorem to hold, for some classes of operators between L(alpha)-spaces, 1 less-than-or-equal-to alpha < + infinity. These results apply in particular to contractions on L2. Some random fields extensions are also studied.