一类单参数的局部时条件过程：广义布朗窃贼
A one-parameter family of local-time conditioned processes : the generalized Brownian burglars
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中文总结 AI 辅助
该研究构造了一类单参数广义布朗窃贼过程，刻画其性质，与相关流理论关联，可处理负强度并推导关键性质。
中文摘要 AI 辅助
我们构造并刻画了一类单参数实值过程，该过程可在实线上给定任意强度的布朗环汤的占有时间场的条件下，恢复其分布规律。这些过程是Warren和Yor构造的布朗窃贼的推广（当强度趋于0且仅存在一个布朗运动时，对应于我们的过程）。这些过程与Bass-Burdzy流以及Aïdékon、Hu和Shi近期关于随机雅可比流的工作密切相关。我们的方法基于驱动过程的概念构建形式体系，其中将研究对象视为我们“拉伸”的直线，而非窃贼本身及其剩余占有时间。这使得我们能通过简单自然的公理来刻画这些（广义）布朗窃贼，还能处理“负强度”，并相当直接地推导窃贼的若干性质，特别是在局部时为高斯自由场平方的特殊强度下的“目标独立性/局部性”性质。
英文摘要
We construct and characterize the one-parameter family of real-valued processes that allow to recover the law of a Brownian loop-soup of any intensity on the real line conditionally on its occupation time field. These processes generalize the Brownian burglar constructed by Warren and Yor (that corresponds to our process in the limiting case where the intensity vanishes and there is just one Brownian motion). These processes are closely related to the Bass-Burdzy flow and recent work of Aïdékon, Hu and Shi on the stochastic Jacobi flow. Our approach uses a formalism, building on the notion of driver processes, where one considers the evolving object to be the line that we ``stretch", instead of the burglar itself and its remaining occupation time. This leads to a characterization of these (generalized) Brownian burglars by simple natural axioms. It also allows to treat ``negative intensities'' and provides fairly direct derivations of several properties of the burglars, and in particular a ``target-independence/locality" property at the special intensity where the local time is the square of a Gaussian Free Field.
发表机构
- University of Cambridge（剑桥大学）
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