Banach Random Walk in the Unit Ball \(S\subset l^{2}\) and Chaotic Decomposition of 详细信息    查看全文

• 作者：Tadeusz Banek
• 关键词：Random walk ; Orthogonal expansion ; Legendre polynomials
• 刊名：Journal of Theoretical Probability
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：29
• 期：4
• 页码：1728-1735
• 全文大小：405 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Statistics
  
• 出版者：Springer Netherlands
• ISSN：1572-9230
• 卷排序：29

文摘

A Banach random walk in the unit ball S in \(l^{2}\) is defined, and we show that the integral introduced by Banach (Theory of the integral. Warszawa-Lwów, 1937) can be expressed as the expectation with respect to the measure \({{\mathbb {P}}}\) induced by this walk. A decomposition \(l^{2}\left( S,{{\mathbb {P}}}\right) =\bigoplus _{i=0}^{\infty } {{\mathfrak {B}}}_{i}\) in terms of what we call Banach chaoses is given.