http://www.mathunion.org/Prizes/2006/gauss_popular_eng.pdfItô's theory is sufficiently abstract to apply to fields that are completely different from the motion of dust in water. Stock prices on the financial market are subject to random forces not unlike those that act in a Brownian motion. Bankers who try to counteract the effects of those fluctuations find themselves forced to trade "in continuous time", at least in theory. Out of Itô's ideas grew a strategy for continuous trading and, eventually, a formula to calculate the price of an option. Today the Black-Scholes formula underlies almost all financial transactions that involve options or futures; moreover, it won two of its inventors the 1997 Nobel prize in economics.
Beyond particle positions and share prices, Itô's theory applies also to the size of a population of living organisms, to the frequency of a certain allele within the gene pool of a population, or even more complex biological quantities. Due to Itô's work, biologists can assess the probability with which a gene will dominate the whole population or a species will survive.
It took mathematicians themselves quite a while to appreciate the importance of Itô's results. This is partially due to Japan's isolation during World War II. Only from 1954 on, Itô lectured on his achievements at the Institute for Advanced Study in Princeton.
Today, there is no doubt that stochastic analysis is a rich, important and fruitful branch of mathematics with a formidable impact to "technology, business, or simply people’s everyday lives".