LARGE DEVIATION RATES FOR BRANCHING PROCESSES-I. SINGLE TYPE CASE
成果类型：
Article
署名作者：
Athreya, K. B.
署名单位：
Iowa State University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004971
发表日期：
1994
页码：
779-790
关键词：
摘要：
Let {Z(n)}(0)(infinity) be a Galton-Watson branching process with offspring distribution {p(j)}(0)(infinity). We assume throughout that p(0) = 0, pj = 0, p(j) not equal 1 for any j >= 1 and 1 < m = Sigma jp(j) < infinity. Let W-n = Z(n) m (-n) and W-n = lim(n) W-n. In this paper we study the rates of convergence to zero as n -> infinity of P( vertical bar Z(n+1)/z(n) - m vertical bar > epsilon), P(vertical bar W-n - W vertical bar > epsilon), P( vertical bar Z(n+1)/z(n) - m vertical bar > epsilon vertical bar W >= a) for epsilon > 0 and a > 0 under various moment conditions on {p(j)}. It is shown that the rate for the first oue is geometric if p(1) > 0 and supergeometric p(1) = 0, while rartes for the other two are always supergemetric under a finite moment generating functions hypothesis.
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