PERTURBATION OF NORMAL RANDOM VECTORS BY NONNORMAL TRANSLATIONS, AND AN APPLICATION TO HIV LATENCY TIME DISTRIBUTIONS
成果类型：
Article
署名作者：
Berman, Simeon M.
署名单位：
New York University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004899
发表日期：
1994
页码：
968-980
关键词：
摘要：
Let Z be a normal random vector in R-k and let 1 be the element of R-k with equal components 1. Let X be a random variable that is independent of Z and consider the sum Z + X 1. The latter has a normal distribution in Rk if and only if X has a normal distribution in R1. The first result of this paper is a formula for a uniform bound on the difference between the density function of Z + X1 and the density function in the case where X has a suitable normal distribution. This is applied to a problem in the theory of stationary Gaussian processes which arose from the author's work on a stochastic model for the CD4 marker in the progression of HIV.