was a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, noted for his contributions to the study of

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appe ...

. The Euler–Maruyama method for the numerical solution of stochastic differential equations bears his name. Maruyama was born in 1916 and graduated from Tohoku University, where he studied Fourier analysis and physics. He began his mathematical work with a paper on Fourier analysis in 1939. He became interested in probability theory through the study of

Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...

's work. He was appointed Assistant professor at the Kyushu University in 1941. When

Kiyosi Itô was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the fo ...

published his papers on stochastic differential equations in 1942, Maruyama immediately recognized the importance of this work and soon published a series of papers on stochastic differential equations and Markov processes. Maruyama is known in particular for his 1955 study of the convergence properties of the finite-difference approximations for the numerical solution of stochastic differential equations, now known as the Euler–Maruyama method. In harmonic analysis, he studied the ergodicity and mixing properties of stationary stochastic processes in terms of their spectral properties. Maruyama also studied quasi-invariance properties of the Wiener measure, extending previous work by Cameron and Martin to diffusion processes.

References

External links

Gisiro Maruyama / Eugene B. Dynkin Collection of Mathematic Interviews / Cornell University Library
20th-century Japanese mathematicians Probability theorists 1916 births 1986 deaths {{Asia-mathematician-stub