In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus is also called the stochastic calculus of variations. P. Malliavin first initiated the calculus on infinite dimensional space. Then, the significant contributors such as S. Kusuoka, D. Stroock, J-M. Bismut, Shinzo Watanabe, I. Shigekawa, and so on finally completed the foundations.
Kalyanapuram Rangachari Parthasarathy was an Indian statistician who was professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient of the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.
James Ritchie Norris is a mathematician working in probability theory and stochastic analysis. He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge.
In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞. In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too.
Sergio Albeverio is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis, mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
Karl-Theodor "Theo" Sturm is a German mathematician working in stochastic analysis.
Jean-Claude Falmagne is a mathematical psychologist whose scientific contributions deal with problems in reaction time theory, psychophysics, philosophy of science, measurement theory, decision theory, and educational technology. Together with Jean-Paul Doignon, he developed knowledge space theory, which is the mathematical foundation for the ALEKS software for the assessment of knowledge in various academic subjects, including K-12 mathematics, chemistry, and accounting.
Kalyan Bidhan Sinha is an Indian mathematician. He is a professor at the Jawaharlal Nehru Centre for Advanced Scientific Research, and Professor Emeritus for life of the Indian Statistical Institute.
Yuri Kondratiev was a Ukrainian mathematician and a professor at the Bielefeld University in Germany.
Alison Mary Etheridge is Professor of Probability and former Head of the Department of Statistics, University of Oxford. Etheridge is a fellow of Magdalen College, Oxford.
Shinzō Watanabe is a Japanese mathematician, who has made fundamental contributions to probability theory, stochastic processes and stochastic differential equations. He is regarded and revered as one of the fundamental contributors to the modern probability theory and Stochastic calculus. The pioneering book “Stochastic Differential Equations and Diffusion Processes” he wrote with Nobuyuki Ikeda has attracted a lot of researchers into the area and is known as the “Ikeda-Watanabe” for researchers in the field of stochastic analysis. He had been served as the editor of Springer Mathematics.
Kavita Ramanan is a probability theorist who works as a professor of applied mathematics at Brown University.
Paul Robert Chernoff was an American mathematician, specializing in functional analysis and the mathematical foundations of quantum mechanics. He is known for Chernoff's Theorem, a mathematical result in the Feynman path integral formulation of quantum mechanics.
In probability theory, a branch of mathematics, white noise analysis, otherwise known as Hida calculus, is a framework for infinite-dimensional and stochastic calculus, based on the Gaussian white noise probability space, to be compared with Malliavin calculus based on the Wiener process. It was initiated by Takeyuki Hida in his 1975 Carleton Mathematical Lecture Notes.
Zuowei Shen is a Chinese mathematician, and Tan Chin Tuan Centennial Professor at the National University of Singapore (NUS). Shen received his BSc in 1982 from Hohai University (China), MSc in 1987 and PhD in 1991 from University of Alberta. He first joined NUS as a lecturer at the Department of Mathematics in 1993; was promoted to professor in 2002 and distinguished professor in 2009. Shen was Head of Department of Mathematics from 2012 to 2014 and was appointed Dean of Science in 2014.
Leonard Gross is an American mathematician and Professor Emeritus of Mathematics at Cornell University.
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of connections modulo gauge transformations. This situation contrasts with the four-dimensional case, where a rigorous construction of the theory as a measure is currently unknown.
Ambar Niel Sengupta is an Indian-American mathematician. He is a professor of mathematics at the University of Connecticut.
Vladimir Igorevich Bogachev is an eminent Russian mathematician and Full Professor of the Department of Mechanics and Mathematics of the Lomonosov Moscow State University. He is an expert in measure theory, probability theory, infinite-dimensional analysis and partial differential equations arising in mathematical physics. His research was distinguished by several awards including the medal and the prize of the Academy of Sciences of the Soviet Union (1990); Award of the Japan Society for the Promotion of Science (2000); the Doob Lecture of the Bernoulli Society (2017); and the Kolmogorov Prize of the Russian Academy of Sciences (2018).
Hui-Hsiung Kuo is a Taiwanese-American mathematician, author, and academic. He is Nicholson Professor Emeritus at Louisiana State University and one of the founders of the field of white noise analysis.
