The mathematical work of masatoshi fukushima - An essay

Over more than five decades Professor Fukushima has made remarkable contributions to mathematics, especially to stochastic analysis and its applications to science, in particular to mathematical physics. For many of his colleagues, students and friends it becomes an excellent opportunity to express their appreciation of himself and his work by celebrating his Sanju, the 80th birthday in the Japanese tradition, with an international conference and by publishing a Festschrift in his honour. Naturally such a Festschrift should contain a scientific account of Professor Fukushima’s oeuvre. When making here an attempt, i.e. writing “un essai” in the classical meaning, to present such an account, we must be aware that we are not discussing a completed oeuvre. Professor Fukushima is continuing to make highly original research contributions with deep insights. Obviously it is pre-matured to describe or guess the lasting impact these latest contributions will have. However it is fair to say that some of his earlier works are meanwhile considered as to belong to the “classical canon” of stochastic analysis, and hence we will concentrate more on those contributions. But we will see how some of his latest research indeed connect with his earlier work in a natural way.