ON THE FILTRATION OF HISTORICAL BROWNIAN-MOTION

• 成果类型: Article
• 署名作者: BARLOW, MT; PERKINS, EA
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988603
• 发表日期: 1994
• 页码: 1273-1294
• 关键词: nonlinear differential-equations; valued branching diffusions; heat-equation; PROPERTY

摘要

We show that the historical Brownian motion may be recovered from ordinary super-Brownian motion when the dimension d of the underlying Brownian motion is greater than 4. We outline a proof showing that this conclusion is false if d less than or equal to 3. The state of affairs in the critical dimension d = 4 is left unresolved. Some extensions are given for 1+beta stable branching mechanisms where beta epsilon (0, 1).