论文标题
适应的拓扑和更高的排名签名
Adapted Topologies and Higher Rank Signatures
论文作者
论文摘要
弱收敛的拓扑并不能解释在适应性随机过程过滤中捕获的信息的增长。例如，两个改编的随机过程可以具有非常相似的定律，但在最佳停止，排队理论或随机编程等应用中给出了完全不同的结果。为了解决此类不连续性，Aldous引入了扩展的弱拓扑，随后，胡佛和Keisler表明，弱拓扑和扩展的弱拓扑都只是一系列拓扑结构的前两个拓扑，这些拓扑变得越来越细。我们使用较高的等级预期特征将适应的过程嵌入到分级的线性空间中，并表明这些嵌入会诱导胡佛 - 凯斯勒的适应性拓扑。
The topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. For example, two adapted stochastic processes can have very similar laws but give completely different results in applications such as optimal stopping, queuing theory, or stochastic programming. To address such discontinuities, Aldous introduced the extended weak topology, and subsequently, Hoover and Keisler showed that both, weak topology and extended weak topology, are just the first two topologies in a sequence of topologies that get increasingly finer. We use higher rank expected signatures to embed adapted processes into graded linear spaces and show that these embeddings induce the adapted topologies of Hoover--Keisler.
