Studies on Noncausal Problems in Mathematical Sciences

在数学科学的各个领域，包括金融理论，出现了许多非因果性质的问题，不能在通常的伊藤微积分理论中处理，而是在作者于1893年创立的非因果微积分框架中处理。在本研究计划中，我们的目的是探讨该理论的理论背景以及与金融有关的一些数值问题。在这两个方向上，我们已经获得了许多基本的理论结果和数值方案，这些都发表在期刊上，并在许多国际会议上提出。

In various fields of mathematical sciences, including theory of finance, there arise many problems of noncausal nature that can be treated not in theusual theory of Ito Calculus but in the framework of noncausal calculus originated by the author in 1893. In this research program we have aimed to investigate the theoretical back ground of the theory as well as some numerical problems concerned with the finance. In both directions, we have obtained many fundamental theoretical results and numerical schemes, those were published in journals and presented at many international conferences.