Ito Integrals

Abstract

Kiyoshi Ito (1915–2008) was awarded the inaugural Gauss Prize by the International Mathematical Union in 2006. Stochastic integration in the narrow sense can be traced back to his early work published in Japanese in the forties of the last century. We precede the general definition of the Ito integral with a special case. Concluding, we discuss the (quadratic) variation of a process without which a sound understanding of Ito’s lemma will not be possible.