Martingales associated to peacocks using the curtain coupling
Martingales associated to peacocks using the curtain coupling
复制标题
使用窗帘耦合与孔雀相关的鞅
DOI：
10.1214/18-ejp138
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发表时间：
2018
影响因子：
1.4
通讯作者：
N. Juillet
中科院分区：
文献类型：
--
作者：
N. Juillet
我们考虑右连续孔雀族，即真实的概率测度族（μt）t∈[0，1]按凸序递增.给定一个时间分割序列，我们将鞅序列联系起来，其特征在于它们是马尔可夫的，在分割区间[tk，tk+1]上是常数，并且使得在时间tk+1的转移核是边际μtk和μtk+1的窗帘耦合。我们研究了分区网格趋于零时的极限幕过程，并研究了其存在性、唯一性和与原始数据的相关性。对于任何右连续孔雀，我们证明存在序列的分区，使一个极限过程存在（有限维收敛）。在某些额外的正则性假设下，证明了存在唯一的极限幕过程，并且它是一个马氏鞅。我们首先用初等方法研究孔雀，孔雀的边缘对应于凸阶的均匀分布。在这种情况下，结果和技术完成的结果和技术中使用的一个平行的工作由亨利-埃德尔，谭和Touzi [9]。我们得到了与一类解析离散孔雀有关的所有极限幕过程的相同类型的结果，测量μt是可解支持的，并且在t中解析地变化。最后，我们给出了孔雀和序列的划分，使极限窗帘过程是一个非马尔可夫鞅的例子。
We consider right-continuous peacocks, that is, families of real probability measures (μt)t∈[0,1] that are increasing in convex order. Given a sequence of time partitions we associate the sequence of martingales characterised by the fact that they are Markovian, constant on the partition intervals [tk, tk+1[, and such that the transition kernels at times tk+1 are the curtain couplings of marginals μtk and μtk+1 . We study the limit curtain processes obtained when the mesh of the partition tends to zero and study existence, uniqueness and relevancy with respect to the original data. For any right-continuous peacock we show there exist sequences of partitions such that a limit process exists (for the finite-dimensional convergence). Under certain additional regularity assumptions, we prove that there is a unique limit curtain process and that it is a Markovian martingale. We first study by elementary methods peacocks whose marginals correspond to uniform distributions in convex order. In this case, the results and techniques complete the results and techniques used in a parallel work by Henry-Labordère, Tan and Touzi [9]. We obtain the same type of results for all limit curtain processes associated to a class of analytic discrete peacocks, i.e., the measures μt are finitely supported and vary analytically in t. Finally, we give examples of peacocks and sequences of partitions such that the limit curtain process is a non-Markovian martingale.
影响因子：
3.1
作者：
Beiglboeck, Mathias;Cox, Alexander M. G.;Huesmann, Martin
通讯作者：
Huesmann, Martin