A Skorohod representation theorem for uniform distance

作者：Berti Patrizia; Pratelli Luca; Rigo Pietro^*

来源：Probability Theory and Related Fields, 2011, 150(1-2): 321-335.

DOI：10.1007/s00440-010-0279-6

• Cadlag function
• Exchangeable empirical process
• Separable probability measure
• Skorohod representation theorem
• Uniform distance
• Weak convergence of probability measures

Let mu (n) be a probability measure on the Borel sigma-field on D[0, 1] with respect to Skorohod distance, n a parts per thousand yen 0. Necessary and sufficient conditions for the following statement are provided. On some probability space, there are D[0, 1]-valued random variables X (n) such that X (n) similar to mu (n) for all n a parts per thousand yen 0 and ||X (n) - X (0)|| -> 0 in probability, where ||center dot|| is the sup-norm. Such conditions do not require mu (0) separable under ||center dot||. Applications to exchangeable empirical processes and to pure jump processes are given as well.

• 出版日期2011-6