SOME LIMIT-THEOREMS FOR SUPER-BROWNIAN MOTION AND SEMILINEAR DIFFERENTIAL-EQUATIONS

• 成果类型: Article
• 署名作者: LEE, TY
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989278
• 发表日期: 1993
• 页码: 979-995
• 关键词: large deviations; systems

摘要

The empirical measure, a generalization of occupation times, of a super-Brownian motion is studied. In our case the empirical measure tends almost surely to Lebesgue measure as time t --> infinity. Asymptotic probabilities of deviation from this central behavior by various orders (large, not very large and normal deviations) are estimated. Extension to similar superprocesses, that is, Dawson-Watanabe processes, is discussed. Our analytic approach also produces new results for semilinear PDE's.