Large deviations for the three-dimensional super-Brownian motion

• 成果类型: Article
• 署名作者: Lee, TY; Remillard, B
• 署名单位: University of Quebec; University of Quebec Trois Rivieres
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987802
• 发表日期: 1995
• 页码: 1755-1771
• 关键词: occupation time; diffusion; EQUATIONS; systems

摘要

Let mu(t)(dx) denote a three-dimensional super-Brownian motion with deterministic initial state mu(0)(dx) = dx, the Lebesgue measure. Let V: R(3) --> R be Holder-continuous with compact support, not identically zero and such that integral(R3)V(x) dx = 0. We show that log P {integral(0)(t) integral(R3)V(x)mu(s)(dx)ds > bt(3/4)} is of order t(1/2) as t --> infinity, for b > 0. This should be compared with the known result for the case integral(R3)V(x)dx > 0. In that case the normalization bt(3/4), b > 0, must be replaced by bt, b > integral(R3)V(x)dx, in order that the same statement hold true. While this result only captures the logarithmic order, the method of proof enables us to obtain complete results for the corresponding moderate deviations and central limit theorems.