Abstract
In this paper, long-time and high-order moment asymptotics for super-Brownian motions (sBm’s) are studied. By using a moment formula for sBm’s (e.g. (Ann. Appl. Probab. 33 (2023) 3872–3915, Theorem 3.1)), precise upper and lower bounds for all positive integer moments at any time of sBm’s for certain initial conditions are achieved. Then, the moment asymptotics as time goes to infinity or as the moment order goes to infinity follow immediately. Additionally, as an application of the two-sided moment bounds, the tail probability estimates of sBm’s are obtained.
Funding Statement
Y. Hu is supported by an NSERC Discovery grant and a centennial fund from University of Alberta. X. Wang is supported by a research fund from Johns Hopkins University. P. Xia is supported by NSF grant DMS-2246850. J. Zheng is supported by NSFC grant 11901598 and Guangdong Characteristic Innovation Project No.2023KTSCX163.
Citation
Yaozhong Hu. Xiong Wang. Panqiu Xia. Jiayu Zheng. "Moment asymptotics for super-Brownian motions." Bernoulli 30 (4) 3119 - 3136, November 2024. https://doi.org/10.3150/23-BEJ1708
Information
