QUADRATURE ROUTINES FOR LADDER VARIABLES
成果类型：
Article
署名作者：
Keener, Robert W.
署名单位：
University of Michigan System; University of Michigan
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005073
发表日期：
1994
页码：
570-590
关键词：
摘要：
Let T = inf{n >= 1: S-n > 0} and H = S-T be ladder variables for a random walk {S-n}(n >= 1) with nonnegative drift. Integral formulas for generating functions and moments of T, H and related quantities are developed. These formulas are suitable for numerical quadrature and should be easier to implement than formulas based on Spitzer's identity when the distribution of S-n is complicated. The approach used makes key use of the Hilbert transform and the main regularity assumption is that some power of the characteristic function for steps of the random walk is integrable.