NECESSARY AND SUFFICIENT CONDITIONS FOR SAMPLE CONTINUITY OF RANDOM FOURIER-SERIES AND OF HARMONIC INFINITELY DIVISIBLE PROCESSES

• 成果类型: Article
• 署名作者: TALAGRAND, M
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989916
• 发表日期: 1992
• 页码: 1-28
• 关键词: strongly stationary-processes

摘要

For very general random Fourier series and infinitely divisible processes on a locally compact Abelian group G, a necessary and sufficient condition for sample continuity is given in terms of the convergence of a certain series. This series expresses a control on the covering numbers of a compact neighborhood of G by certain nonrandom sets naturally associated with the Fourier series (resp. the process). In the nonstationary case, we give a necessary Sudakov-type condition for a probability measure in a Banach space to be a Levy measure.