Kiyoshi Ito, a mathematician whose innovative models of random motion are used today in fields as diverse as finance and biology, died Nov. 10 at a hospital in Kyoto, Japan. He was 93.

His death was confirmed by his daughter, Junko Ito.

Mr. Ito is known for his contributions to probability theory, the study of randomness. His work, starting in the 1940s, built on the earlier breakthroughs of Albert Einstein and Norbert Wiener. Mr. Ito’s mathematical framework for describing the evolution of random phenomena came to be known as the Ito Calculus.

“People all over realized that what Ito had done explained things that were unexplainable before,” said Daniel Stroock, a professor of mathematics at the Massachusetts Institute of Technology.

Mr. Ito’s research was theoretical, but his models served as a tool kit for others, notably in finance. Robert C. Merton, a winner of the Nobel in economic science, said he found Mr. Ito’s model “a very useful tool” in his research on the evolution of stock prices in a portfolio and, later, in helping develop a theory for pricing stock options that is used on Wall Street today. Mr. Ito, he said, was “a very eminent mathematician.”