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Kiyosi Itô

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Kiyosi Itô

Itô at

, 1970

Born

September 7, 1915

Died

November 10, 2008

(aged 93)

Alma mater

Known for

Awards

(1977)

(1987)

(1998)

(2006)

Scientific career

Fields

Institutions

Doctoral

students

Kiyosi Itô

(

伊藤清

Itō Kiyoshi

;

Japanese pronunciation:

, 7

September 1915 – 10 November 2008)

was a

who made

fundamental contributions to

, in particular, the theory of

. He invented the concept of

and

, and is known as the founder of so-called

. He also pioneered the connections between stochastic calculus and

differential geometry, known as

. He was

invited for the

1962.

So much were

Itô's results useful to financial mathematics that he

was sometimes called "the most famous Japanese in Wall Street".

Itô was a member of the faculty at

for most of his career

and eventually became the director of their

But he also spent multi-year stints at several foreign

institutions, the longest of which took place at

Overview

[

]

Itô (right) with Issei

Shiraishi in 1935. Shiraishi

later became a mathematician.

Itô pioneered the theory of

and

, now known as

. Its

basic concept is the

, and among

the most important results is a change of

variable formula known as

(also known as the Itô formula).

Itô

also made contributions to the study of

known as

Itô calculus is a method used in the mathematical study of

and

is applied in various fields, and is perhaps best known for its use in

. In particular, the Itô's lemma's best known application

is in the derivation of the

for option values.

Itô's methods are also used in other fields, including biology and physics.

His results have been applied to

, and

, in addition to uses in various mathematical

subjects such as

, and

and

Fellow mathematician

noted that "People all over realized

that what Ito had done explained things that were unexplainable before."

Economist

stated that

Itô's work had provided him "a very useful tool" in his own prize-winning work.

Although the standard

of his name is

Kiyoshi Itō

, he used the spelling Kiyosi Itô (

). The alternative spellings Itoh and Ito are also sometimes seen in the

Itô was married with three daughters.

Biography

[

]

Kiyosi Itô (right)

with his brother

Seizō Itō in 1937.

Seizō later became a

mathematician.

Itô was born on 7 September 1915 in a farming area located west of

that being

the town of

He excelled in his studies as a youth.

Admitted

to the

, he studied mathematics and became interested in the

underdeveloped field of

, graduating from there in 1938,

with his degree in

mathematics being granted by the

Itô at the Cabinet Statistics

Bureau in 1940

From 1939 to 1943 he worked as a Statistical Officer with the

There he was given rein by

management to continue his research.

His breakthrough paper, "On Stochastic

Processes", appeared in 1942.

In 1943, he was appointed an assistant professor at

where he benefited from discussions with the

mathematicians

and

From investigations done during this period he published a series

of articles in which he defined the

and laid the foundations of the

Meanwhile, he

received his

degree from the Imperial University of Tokyo in 1945.

These works were published despite the difficulties of life in

, including problems accessing

libraries and especially the loss of contact with Western mathematicians and the lack of awareness of results from

them.

For instance, the only other Japanese mathematician actively interested in

Itô's work during the war,

, read a mimeographed copy of a paper while in a military camp.

Scholarly activity during the

had its difficulties; in one case, paper shortages were such that a lengthy Itô article could not

be published in a Japanese journal and he had to arrange for an American journal to publish it instead.

Ito later

referred to his time at Nagoya as having been during "the dark age of World War II and its aftermath."

Itô, 1954

After this period he continued to develop his ideas on stochastic analysis with many important

papers on the topic. In 1952, he became a professor at the

His most

well-known text,

Probability Theory

, appeared in 1953.

Itô

remained affiliated with Kyoto

until his retirement in 1979.

However, beginning in the 1950s, Itô spent long periods of time

away from Japan.

He was at the

from 1954 to 1956 while on a

;

while there he worked closely with

and

who were at nearby

He was

a professor at

from 1961 to 1964 and a professor at

from 1966 to 1969.

Then in 1969 Itô arrived at

, where he was a professor of mathematics for six years until 1975.

This was his longest stint outside Japan.

Among the courses he taught at Cornell was one in Higher Calculus.

Itô wrote not only in

but also in

and

However, his ability to converse in

foreign languages was a different matter, and by his own admission his accent made him largely incomprehensible to

Americans.

When Itô left Cornell and returned to the University of Kyoto, he served as director of their

After his retirement, he became professor emeritus at Kyoto University.

He also had a

post-retirement position as a professor at the private

for several years,

a common practice

among higher-ranking Japanese academics.

Itô c. 1991

Itô

was recipient of the

and the

He was a member of the

and also a foreign member of the

in France and the

in the United States.

In his later years, Itô struggled with poor health.

Itô was awarded the inaugural

in 2006 by the

for his lifetime achievements.

As he due to his health was unable to travel to

, his youngest daughter,

, received the Gauss Prize from

on his behalf.

Later, IMU

President

personally presented the medal to Itô at a special ceremony held in Kyoto.

October 2008, Itô was honored with Japan's

, and an awards ceremony for the Order of Culture was held

at the Imperial Palace.

Itô died on November 10, 2008, in

, at age 93, of

Selected publications

[

]

Kiyosi Itô (1940).

. 3rd Series.

(12):

977–

998.

Kiyosi Ito (1942).

(PDF)

(1077):

1352–

1400.

Kiyosi Itô (1944).

(8):

519–

524.

Kiyosi Itô (1946).

(2):

32–

35.

Kiyosi Itô (1950).

35–

47.

Kiyosi Itô (1951).

55–

65.

Kiyosi Itô and Henry McKean (1974).

Diffusion Processes and Their Sample Paths

. Berlin:

Kiyosi Itô (1984).

. Philadelphia:

References

[

]

. Retrieved

16 June

2024

. 15 November 2008.

Protter, Philip (June–July 2007).

(PDF)

Notices of the American Mathematical Society

(6):

744–

745.

Lohr, Steve (23 November 2008),

. London. 20 November 2008.

Retrieved

8 January

2009

DiPietro, Louis (17 April 2024).

Itô, Kiyosi (2014) [1987]. "Foreword". In Stroock, D. W.; Varadhan, S. R. S. (eds.).

Kiyosi Itô Selected Papers

. New

York: Springer-Verlag. pp.

xiii–

xvii.

Subsequently reproduced in

Chern, S S; Hirzebruch, F, eds. (2000).

. Vol. 1. Singapore: World Scientific. pp.

531–

535.

Cornell University Announcements: College of Arts and Sciences, 1974–75

. Cornell University. 1 July 1974. p. 127.

. Retrieved

16 June

2024