标题： 具有半连续协方差的随机过程的最优设计、金融和风险建模 显示英文标题

标题： Optimal design, financial and risk modelling with stochastic processes having semicontinuous covariances

摘要： A.N. 柯尔莫戈洛夫提出了几个关于随机过程的问题，后来很少有人关注这些问题。其中一个未解决的问题是具有不连续协方差函数的随机过程。例如，半连续协方差函数最近被许多统计学家用于回归和克里金方法。本文引入了纯粹基于拓扑定义的协方差核正则性条件，这些条件仍然适用于回归问题、克里金方法以及金融领域的渐近分析。这些条件与奥恩斯坦-乌伦贝克（OU）过程的半连续映射有关。除此之外，这些新的正则性条件通过考虑半连续协方差放松了协方差函数的连续性。我们还介绍了所提出类别的几种新颖应用，包括随机场的最优设计、金融中的随机游走以及与地震等冲击相关的破产概率。特别是，我们构建了一个具有半连续协方差的随机游走模型。 显示英文摘要

摘要： A.N. Kolmogorov proposed several problems on stochastic processes, which has been rarely addressed later on. One of the open problems are stochastic processes with discontinuous covariance function. For example, semicontinuous covariance functions have been used in regression and kriging by many authors in statistics recently. In this paper we introduce purely topologically defined regularity conditions on covariance kernels which are still applicable for increasing and infill domain asymptotics for regression problems, kriging and finance. These conditions are related to semicontinuous maps of Ornstein Uhlenbeck (OU) processes. Beside this new regularity conditions relax the continuity of covariance function by consideration of semicontinuous covariance. We provide several novel applications of the introduced class for optimal design of random fields, random walks in finance and probabilities of ruins related to shocks, e.g. by earthquakes. In particular we construct a random walk model with semicontinuous covariance.