Pathwise integration, Malliavin calculus and stochastic control

路径积分、Malliavin 微积分和随机控制

• 批准号: 1783872
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1783872
• 关键词: Pathwise; integration; Malliavin; calculus; stochastic

This project is concerned with the development of pathwise integration techniques in the scope of Malliavin calculus. The main applications will be new classifications for stochastic processes, development of new numerical methods and new theoretical developments in stochastic optimal control taking advantage of the new pathwise interpretation paradigm. The project takes inspiration in the marriage between analysis and probability by creating and developing tools specific to one field and applying them to the other. The project leads lastly to applications in path-dependent partial differential equations. These appear naturally within the scope of stochastic optimal control problems involving so-called path-dependent contracts when using the pathwise technique. Addressed is also the deeper issue of giving meaning to martingales from a pathwise point of view.

该项目涉及 Malliavin 微积分范围内的路径积分技术的开发。主要应用将是随机过程的新分类、新数值方法的开发以及利用新的路径解释范式的随机最优控制的新理论发展。该项目通过创建和开发特定于一个领域的工具并将其应用于另一领域，从分析与概率的结合中汲取灵感。该项目最终导致了路径相关偏微分方程的应用。当使用路径技术时，这些自然出现在涉及所谓路径依赖契约的随机最优控制问题的范围内。还解决了从路径角度赋予鞅意义的更深层次问题。

项目成果

Differentiability of SDEs with drifts of super-linear growth

• DOI: 10.1214/18-ejp261
• 发表时间: 2018-03
• 期刊: Electronic Journal of Probability
• 影响因子: 1.4
• 作者: P. Imkeller;Gonccalo dos Reis;William Salkeld

Small ball probabilities, metric entropy and Gaussian rough paths

小球概率、度量熵和高斯粗糙路径

• DOI: 10.1016/j.jmaa.2021.125697
• 发表时间: 2022
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: Salkeld W