Exact packing measure of the range of -Super Brownian motions

• 成果类型: Article
• 署名作者: Duhalde, Xan; Duquesne, Thomas
• 署名单位: Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0680-2
• 发表日期: 2017
• 页码: 201-252
• 关键词: hausdorff measure; support

摘要

We consider super processes whose spatial motion is the d-dimensional Brownian motion and whose branching mechanism is critical or subcritical; such processes are called -super Brownian motions. If , where is the lower index of at , then the total range of the -super Brownian motion has an exact packing measure whose gauge function is , where . More precisely, we show that the occupation measure of the -super Brownian motion is the g-packing measure restricted to its total range, up to a deterministic multiplicative constant only depending on d and . This generalizes the main result of Duquesne (Ann Probab 37(6):2431-2458, 2009) that treats the quadratic branching case. For a wide class of , the constant is shown to be equal to the packing dimension of the total range.