Pathwise integration, Malliavin calculus and stochastic control

这个项目是关于路径积分技术的发展，在马利亚文微积分的范围。主要应用将是随机过程的新分类，新的数值方法的发展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个领域，从分析和概率之间的结合中获得灵感。该项目最后导致在路径相关偏微分方程中的应用。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。从路径的角度来看，这也涉及到赋予鞅意义的更深层次的问题。

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.