In this article, we prove integration by parts formulae (IbPFs) for the laws of Bessel bridges from 0 to 0 over the interval [0, 1] of dimension smaller than 3. As an application, we construct a weak version of a stochastic PDE having the law of a one-dimensional Bessel bridge (i.e. the law of a reflected Brownian bridge) as reversible measure, the dimension 1 being particularly relevant in view of applications to scaling limits of dynamical critical pinning models. We also exploit the IbPFs to conjecture the structure of the stochastic PDEs associated with Bessel bridges of all dimensions smaller than 3.

中文翻译：

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贝塞尔 SPDE 和重新归一化的本地时间

在本文中，我们证明了在小于 3 的维数区间 [0, 1] 上从 0 到 0 的贝塞尔桥定律的分部公式 (IbPF) 积分。作为一个应用，我们构建了一个弱版本的随机偏微分方程将一维贝塞尔电桥定律​​（即反射布朗电桥定律）作为可逆测度，考虑到动态临界钉扎模型的缩放限制的应用，维度 1 特别相关。我们还利用 IbPF 来推测与所有尺寸小于 3 的贝塞尔桥相关的随机偏微分方程的结构。