一类相互作用的分支量值扩散的田中公式和局部时间

Pub Date : 2023-12-08 DOI:10.1007/s10114-023-2308-2

Donald A. Dawson, Jean Vaillancourt, Hao Wang

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引用次数: 0

摘要

我们构建了欧几里得空间ℝd中d≥1的依赖空间运动的超过程（SDSM），并证明了即使它们从某些无界的初始正Radon度量（如ℝd上的Lebesgue度量）开始，当d≤3时，它们的局部时间也是存在的。同时还推导出了局部时间的田中公式。

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Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ^d with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ^d, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived.

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