Memoirs of My Research on Stochastic Analysis

Analysis and Applications, which is devoted to my work and its further de-velopments. I would like to thank the symposium organizers for their tireless efforts in organizing this successful symposium and for providing me with the opportunity to present some memoirs of my research on stochastic analysis, which, I hope, will be of some interest to the participants. My doctoral thesis published in 1942 [1] was on a decomposition of the sample path of the continuous time stochastic process with independent in-crements, now called the Lévy–Ito ̂ decomposition of the Lévy process. In the 1942 article written in Japanese [2] and the extended 1951 version that ap-peared in the Memoirs of the American Mathematical Society [3], I succeeded in unifying Lévy’s view on stochastic processes and Kolmogorov’s approach to Markov processes and created the theory of stochastic differential equations and the related stochastic calculus. As is beautifully presented in a recent book by Daniel Stroock [11], Markov Processes from K. Itô’s Perspective, my conception behind those works was to take, in a certain sense, a Lévy pro-cess as a tangent to the Markov process. The above mentioned papers are reprinted in Kiyosi Ito ̂ Selected Papers edited by Stroock and Varadhan [8], and the editors ’ introduction and my own foreword explain in some detail the circumstances leading to their development