Multidimensional Stochastic Models and Their Applications

多维随机模型及其应用

• 批准号: 429659655
• 负责人: Professor Dr. Frank Aurzada
• 金额: --
• 依托单位: Arbeitsgruppe Stochastik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/429659655?language=en
• 关键词: Multidimensional; Stochastic; Models; Their; Applications

The developments of Probability, Statistics, and their applications lead to increasingly complex models, involving a large number of variables as well as hidden or explicit parameters including a variety of random factors as well. The objects of our research like random matrices and random polynomials, Gaussian fields, random polytopes, fractional Laplacians as generators of Levy processes, U-max statistics and kernel density estimators are topics which are currently intensively studied. Research in this area requires the solution of basic open questions in modern Probability and Statistics using techniques relying on the latest mathematical achievements. In particular we shall concentrate on the solution of open problems concerning U-max statistics, the relation of random polytopes and intrinsic volumes to Gaussian random matrices and Gaussian processes, complexity measures for quantization and coding errors and the distribution of fractional processes as well as problems of small deviations.

概率、统计学及其应用的发展导致模型日益复杂，涉及大量变量以及隐藏或显式参数，包括各种随机因素。我们的研究对象包括随机矩阵和随机多项式、高斯场、随机多面体、作为 Levy 过程生成器的分数拉普拉斯算子、U-max 统计量和核密度估计器，这些都是目前正在深入研究的主题。该领域的研究需要使用最新数学成果的技术来解决现代概率和统计中的基本开放问题。特别是，我们将集中精力解决有关 U-max 统计、随机多胞形和本征体积与高斯随机矩阵和高斯过程的关系、量化和编码误差的复杂性度量、分数过程的分布以及小偏差问题等开放问题的解决。