论文标题
任意维度的正规化凯勒勒定理
A regularized Kellerer theorem in arbitrary dimension
论文作者
论文摘要
我们介绍了凯勒勒定理的多维扩展，内容涉及模仿马尔可夫·马尔丁莱斯（Markov Martingales）的孔雀，这是一个源自法语的术语，用于随机过程，以凸的顺序增加。为了在高斯正则化后连续的孔雀在任意维度上，我们表明有强烈的马尔可夫模仿了martingaleitô扩散。 Martingale扩散的新型紧凑性结果是我们证明的关键工具。此外，我们提供反例以在尺寸$ d \ geq 2 $中显示出独特性可能无法保持，并且必须进行一些正规化以确保存在模仿的马尔可夫·马丁格（Markov Martingale）。
We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes increasing in convex order. For a continuous-time peacock in arbitrary dimension, after Gaussian regularization, we show that there exists a strongly Markovian mimicking martingale Itô diffusion. A novel compactness result for martingale diffusions is a key tool in our proof. Moreover, we provide counterexamples to show, in dimension $d \geq 2$, that uniqueness may not hold, and that some regularization is necessary to guarantee existence of a mimicking Markov martingale.
