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On Sets of Laws of Continuous Martingales
Theory of Probability and Its Applications ( IF 0.6 ) Pub Date : 2021-02-05 , DOI: 10.1137/s0040585x97t990198
Yu. M. Kabanov

Theory of Probability &Its Applications, Volume 65, Issue 4, Page 652-655, January 2021.
We prove that the set of laws of stochastic integrals $H\,{\cdot}\, W$, where $W$ is a multidimensional Wiener process and $H^2$ takes values in a compact convex subset $D$ of the set of symmetric positive semidefinite matrices, is weakly dense in the set of laws of martingales $M$ with $d\langle M \rangle/dt$ taking values in $D$.


中文翻译:

关于连续马丁格尔定律集

Theory of Probability & Its Applications,第 65 卷,第 4 期,第 652-655 页,2021 年 1 月。
我们证明了随机积分定律集 $H\,{\cdot}\, W$,其中 $W$ 是一个多维维纳过程和 $H^2$ 取对称正半正定矩阵集合的紧凸子集 $D$ 中的值,在带有 $d\langle M \rangle/dt 的鞅定律集合 $M$ 中是弱稠密的$ 以 $D$ 为单位取值。
更新日期:2021-02-05
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