Sample path large deviations for super-Brownian motion

• 成果类型: Article
• 署名作者: Schied, A
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• 发表日期: 1996
• 页码: 319-347
• 关键词: valued branching-processes; time

摘要

We derive two large deviation principles of Freidlin-Wentzell type for rescaled super-Brownian motion. For one of the appearing rate functions an integral representation is given and interpreted as 'Kakutani-Hellinger energy'. As a tool we develop estimates for the Laplace functionals of (historical) super-Brownian motion and certain maximal inequalities. Also it is shown that the Holder norm of index alpha < 1/2 of the process t --> (f,X(t)) possesses some finite exponential moments provided the function f is smooth.