Content

- Description

- About Kiyosi Itô

- Previous Itô Prize Winners

- Prize Committee

The prize honors the memory and celebrates the legacy of Professor Kiyosi Itô and his seminal contributions to probability theory. It is awarded every two years to the best paper in Stochastic Processes and their Applications published in a period of two years.

### Description

The Itô prize is awarded by the Elsevier journal Stochastic Processes and their Applications to reward a paper recently published in the journal that we feel has significantly advanced the theory or applications of stochastic processes. The prize also has the purpose of honoring the vast and seminal contributions of Professor K. Itô to the subject.

Professor Kiyosi Itô was born on September 7, 1915 in Mie, Japan. In 2003 when the prize was first awarded, he turned 88 years old. In Japan this is a significant birthday, known as one’s “rice birthday,” since the characters for 88 resemble the character for rice. It was thus a fitting time to acknowledge the immense gifts Professor Itô has given to mathematics and to probability theory in particular, by naming this prize in his honor. It is also appropriate to remind ourselves of the contributions Professor Itô has made to the field, and how significant they are.

The prize consists of a monetary award of $USD 5000 and is awarded at the Bernoulli Society Conference on Stochastic Processes and Their Applications celebrated in odd years, where the winner presents the Itô Lecture.

### About Kiyosi Itô

K. Itô was born in 1915, in the prefecture of Mie in Japan. His invention of stochastic calculus is by now a central element in Probability Theory. It took nearly twenty five years for this work, which had been elaborated between 1942 and 1950, to permeate the field until it became a standard topic taught in every course on advanced probability.

In 1970, K. Itô published a second revolutionary paper, in which he developed the theory of excursions of a Markov process. This work immediately inspired new studies, for Brownian excursions in particular, allowing to revisit and extend the pioneering work of Paul Lévy on this topic.

K. Itô is the co-author, with H.P. Mc Kean, of the book *Diffusion Processes and their Sample paths* (1965), which has been extremely influential in the study of diffusion processes, say between 1965 and 1980.

One should also mention Itô's book on infinite-dimensional Markov processes, a topic of which he was particularly fond, as can be seen from the Foreword in *Selected Papers* (1987) in which he writes: *After several years it became my habit to observe even finite-dimensional facts from the infinite-dimensional viewpoint*. Indeed, this viewpoint is extremely fruitful, as Itô's theory of excursions shows very clearly. I consider that Malliavin Calculus hinges upon the same general principle (this is not a very original statement!)

K. Itô has founded an extremely powerful probabilistic school in Japan; among his students let me mention N. Ikeda, H. Kunita, M. Fukushima and S. Watanabe, each of whom had also many students who continued to develop their master's field.

To summarize, K. Itô is one of the greatest probabilists of the twentieth century, in the same vein as P. Lévy and A. Kolmogorov.

(From Kiyosi I Itô remembered (1915-2008), by Marc Yor, Bernoulli News Vol. 16, No 1, May 2009, http://isi.cbs.nl/bnews/09a/index.html). See also http://unjobs.org/authors/kiyosi-ito.

The prize is presented at the SPA conference series, and consists of a monetary award of $5000.

### Previous Itô Prize winners

The Itô Prize 2023 was awarded to Alexander Iksanov and Andrey Pilipenko for the paper On a skew stable Lévy process published in Stochastic Processes and their Applications. Volume 156, February 2023, Pages 44-68.

The Itô Prize 2021 was awarded to Anne van Delft for her paper A note on quadratic forms of stationary functional time series under mild conditions published in Stochastic Processes and their Applications. Volume 130, Issue 7, July 2020, Pages 4206-4251.

The Itô Prize 2019 was awarded to Zhen-Qing Chen and Masatoshi Fukushima, for their paper entitled Stochastic Komatsu-Loewner evolution and BMD domain constant published in Stochastic Processes and their Applications. Volume 128, Issue 2, February 2018, Pages 545-594.

The Itô Prize 2017 was awarded to Noemi Kurt, Adrain G. Casanova, Anton Wakolbinger and Linglong Yuan, for their paper entitled An individual-based model for the Lenski experiment, and the deceleration of the relative fitness published in Stochastic Processes and their Applications. Volume 126, Issue 8, August 2016, Pages 2211-2252.

The Itô Prize 2015 was awarded to Francis Comets and Michael Cranston, for their paper entitled Overlaps and pathwise localization in the Anderson polymer model published in Stochastic Processes and their Applications. Volume 123, Issue 6, June 2013, Pages 2446-2471.

The Itô Prize 2013 was awarded to Hirofumi Osada, for his paper entitled **Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials II: Airy random point field** published in Stochastic Processes and their Applications Volume 123, Issue 3, March 2013, Pages 813-838.

The Itô Prize 2011 was awarded to Nathalie Eisenbaum and Haya Kaspi for their paper entitled **On permanental processes**, published in Stochastic Processes and Applications, Volume 119, Issue 5, May 2009, Pages 1401-1415.

The 2009 Itô Prize was awarded to Marc Wouts for the paper **A coarse graining for the Fortuin-Kasteleyn measure in random media, ***Stochastic Processes and their Applications*, Vol. 118, Issue 11, November 2008, Pages 1929-1972.

The 2007 Itô Prize was awarded to Sylvie Roelly and Michèle Thieullen for the paper **Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts, ***Stochastic Processes and their Applications*, Vol. 15, Issue 10, October 2005, Pages 1167-1700.

The 2005 Itô Prize was awarded to Nicolai V. Krylov for the paper **On weak uniqueness for some diffusions with discontinuous coefficients**, *Stochastic Processes and their Applications*, Vol. 113, Issue 1, September 2004, Pages 37-64.

The first Itô Prize was awarded to Bem Hambly, James Martin and Neil O’Connell for the paper **Concentration results for a Brownian directed percolation problem, ***Stochastic Processes and their Applications*, Vol. 102, Issue 2, December 2002, Pages 207-220.

### Prize Committee

The winning article is selected by the Editorial Board of the journal Stochastic Processes and their Applications*. *