论文标题
关于签名的双态的扩展和内核及其在随机整合中的作用
On the extension and kernels of signed bimeasures and their role in stochastic integration
论文作者
论文摘要
在这项工作中，我们为在$δ$环上扩展签名的双态和相对内核的存在提供了必要和充分的条件。该结果将常规条件概率的构建方法概括为更一般的扩展签名措施的设置。基于这一结果，我们基于随机措施获得了最通用的随机积分理论，从而扩展并推广了著名的Rajput和Rosinski论文中开发的整个整合理论（\ textit {probab。〜theorye lotat。〜fields}，\ textbf {82}（82}}（1989）451-487）和passegger passe passe pascei。 （\ textit {stoch。〜process。〜他们的应用。}，\ textbf {130}，（3），（2020），1735-1791）。
In this work we provide a necessary and sufficient condition for the extension of signed bimeasures on $δ$-rings and for the existence of relative kernels. This result generalises the construction method of regular conditional probabilities to the more general setting of extended signed measures. Building on this result, we obtain the most general theory of stochastic integrals based on random measures, thus extending and generalising the whole integration theory developed in the celebrated Rajput and Rosinski's paper (\textit{Probab.~Theory Relat.~Fields}, \textbf{82} (1989) 451-487) and the recent results by Passeggeri (\textit{Stoch.~Process.~Their Appl.}, \textbf{130}, (3), (2020), 1735-1791).
