A new approach to strong embeddings

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0321-8
• 发表日期: 2012
• 页码: 231-264
• 关键词: finite exponential moments; multidimensional version; invariance-principle; brownian-motion; approximation; sakhanenko; vectors; sums

摘要

We revisit strong approximation theory from a new perspective, culminating in a proof of the Komls-Major-Tusnady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy inequalities. The new technique, inspired by Stein's method of normal approximation, is applicable to any setting where Stein's method works. In particular, one can hope to take it beyond sums of independent random variables.