一维扩散的各种钟的局部时惩罚
Local time penalizations with various clocks for one-dimensional diffusions
摘要：
本文研究了广义一维扩散律的若干极限定理，该扩散律由局部时间的非负函数加权和归一化，并在一个参数化的随机时间族（我们称之为时钟）上求值。由于时钟趋于无穷大，我们表明，初始过程收敛到一个新的惩罚过程，这通常取决于所选择的时钟。然而，与确定性时钟不同，不需要对扩散的预解式进行具体假设。然后，我们通过一些通用的$ σ$ -有限的措施，这些惩罚过程的路径解释。
英文摘要：
We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal $ σ$-finite measures.
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