噪声增强贝塞尔过程的局部时间

Annales Henri Lebesgue Pub Date : 2021-09-26 DOI:10.5802/ahl.151

J. Bertoin

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引用次数: 3

摘要

我们研究了噪声增强对维数为$d\in(0,2)$的贝塞尔过程的影响，特别是对其加性泛函渐近行为的影响。这导致我们引入一个局部时间过程和它的逆过程。我们将后者识别为一个递增的自相似(时间齐次)马尔可夫过程，并由此推导出几个明确的结果。

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On the local times of noise reinforced Bessel processes

We investigate the effects of noise reinforcement on a Bessel process of dimension $d\in(0,2)$, and more specifically on the asymptotic behavior of its additive functionals. This leads us to introduce a local time process and its inverse. We identify the latter as an increasing self-similar (time-homogeneous) Markov process, and from this, several explicit results can be deduced.

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Annales Henri Lebesgue

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