Fixed points of multivariate smoothing transformations

多元平滑变换的不动点

• 批准号: 282184819
• 负责人: Professor Dr. Matthias Meiners
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/282184819?language=en
• 关键词: Fixed; points; multivariate; smoothing; transformations

In various models of applied probability, the limiting distributions of quantities of interest satisfy recursive distributional equations called fixed-point equations of smoothing transformations, the most prominent example being the convolution equation satisfied by the centered normal distributions. While smoothing transformations and their fixed points have been studied extensively in one dimension, only partial results are available in higher dimensions. The goal of the project is to solve large classes of distributional fixed-point equations in higher dimensions, to understand important features of fixed points such as existence, smoothness and decay of densities or the tail behavior of the survival function, and to apply the theoretical results obtained to classical and recent examples.

在各种应用概率模型中，感兴趣量的极限分布满足递归分布方程，即平滑变换的不动点方程，最突出的例子是中心正态分布所满足的卷积方程。虽然在一维上对平滑变换及其不动点进行了广泛的研究，但在高维上只得到部分结果。该项目的目标是在更高的维度上求解大型分布不动点方程，了解不动点的重要特征，如密度的存在性、光滑性和衰减或生存函数的尾部行为，并将所获得的理论结果应用于经典和最近的例子。

项目成果

Convergence of complex martingales in the branching random walk: the boundary

• DOI: 10.1214/17-ecp50
• 发表时间: 2016-11
• 期刊: Electronic Communications in Probability
• 影响因子: 0.5
• 作者: Konrad Kolesko;M. Meiners

Absolute continuity of the martingale limit in branching processes in random environment

• DOI: 10.1214/19-ecp229
• 发表时间: 2018-06
• 期刊: Electronic Communications in Probability
• 影响因子: 0.5
• 作者: E. Damek;N. Gantert;Konrad Kolesko

Solutions to complex smoothing equations

复杂平滑方程的解

• DOI: 10.1007/s00440-016-0709-1
• 发表时间: 2017
• 期刊: Probability Theory and Related Fields
• 影响因子: 2
• 作者: Meiners;Matthias;Mentemeier;Sebastian
• 通讯作者: Sebastian

Fluctuations of Biggins’ martingales at complex parameters

• DOI: 10.1214/20-aihp1046
• 发表时间: 2018-06
• 期刊: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 作者: A. Iksanov;Konrad Kolesko;M. Meiners