Stochastic modelling and network analysis/Modélisation stochastique et analyse de réseaux

随机建模和网络分析/Modelizes stochastique etanalyze de réseaux

• 批准号: RGPIN-2017-04083
• 负责人: Vaillancourt, Jean
• 金额: $ 1.02万
• 依托单位: HEC Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675444
• 关键词: Stochastic; modelling; network; analysis; Mod

The proposed research is composed of several ongoing projects, under the following two unifying themes. ******The main theme is mathematical modelling in situations where nonlinearity and randomness affect the behavior of large numbers of elements in an ensemble, such as the fluctuations in value of commodities on the financial markets. In the discrete case I am specifically interested in strategies leading to the reversal from a collection of losing opportunities for the client, into a winning portfolio through the use of techniques giving rise to the phenomenon called Parrondo's paradox. In the continuous case, nonlinear stochastic partial differential equations (or some associated discrete approximation scheme) in the guise of well-posed martingale problems need to be built, simulated and analyzed via interacting particle systems. My objective for the years to come is the pursuit of my ongoing research projects on the fundamental properties of these systems, which bear potential significance as they extend the applicability of classical limit theory to new mathematical contexts. ******The complementary theme is statistical modelling in the context of knowledge discovery and data mining within certain big data bases, notably heterogeneous information networks of multi-modal data such as social media networks. These require the identification of those mathematical characteristics that best suit a framework of multiple comparisons for the purpose of link prediction and community detection. I plan to incorporate hierarchical structures in the estimation methodology specifically destined for these databases. The novelty here comes from the proposal of new solutions to these issues using advanced data mining and analysis techniques, including formal concept analysis.***********

拟议的研究由以下两个统一主题下的几个正在进行的项目组成。******主要主题是在非线性和随机性影响集合中大量元素行为的情况下的数学建模，例如金融市场上商品价值的波动。在离散的情况下，我特别感兴趣的策略是，通过使用产生Parrondo悖论现象的技术，使客户从一系列失败的机会转变为一个成功的投资组合。在连续情况下，非线性随机偏微分方程（或一些相关的离散近似格式）需要在适定鞅问题的幌子下通过相互作用的粒子系统建立，模拟和分析。我未来几年的目标是追求我正在进行的关于这些系统的基本性质的研究项目，这些项目具有潜在的意义，因为它们将经典极限理论的适用性扩展到新的数学背景。******补充主题是在某些大数据库中知识发现和数据挖掘背景下的统计建模，特别是多模态数据的异构信息网络，如社交媒体网络。这需要识别那些最适合用于链接预测和社区检测的多重比较框架的数学特征。我计划在专门为这些数据库设计的估计方法中加入层次结构。这里的新颖性来自于使用高级数据挖掘和分析技术（包括形式概念分析）提出这些问题的新解决方案。***********