Hilbert space regularity of the (α, d, 1)-superprocess and its occupation time

• 成果类型: Article
• 署名作者: Blount, D; Bose, A
• 署名单位: Arizona State University; Arizona State University-Tempe; Carleton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 104-131
• 关键词: partial-differential equations; diffusion

摘要

The superprocess and its occupation time process are represented as Hilbert space valued solutions of stochastic evolution equations by using the Fourier transform of the process. For appropriate parameter values, the existence of density valued solutions follows. Pathwise regularity of the processes is obtained. As a new tool we develop a maximal inequality. We also extend the Tanaka-like evolution equations developed for local time processes and provide an Ito formula for certain functionals of the superprocess.