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Professor Kiyosi Ito is well known as the creator of the modern
theory of stochastic analysis. Although Ito first proposed his
theory, now known as Ito's stochastic analysis or Ito's stochastic
calculus, about fifty years ago, its value in both pure and applied
mathematics is becoming greater and greater. For almost all modern
theories at the forefront of probability and related fields, Ito's
analysis is indispensable as an essential instrument, and it will
remain so in the future. For example, a basic formula, called the
Ito formula, is well known and widely used in fields as diverse as
physics and economics.
This volume contains 27 papers written by world-renowned
probability theorists. Their subjects vary widely and they present
new results and ideas in the fields where stochastic analysis plays
an important role. Also included are several expository articles by
well-known experts surveying recent developments. Not only
mathematicians but also physicists, biologists, economists and
researchers in other fields who are interested in the effectiveness
of stochastic theory will find valuable suggestions for their
research. In addition, students who are beginning their study and
research in stochastic analysis and related fields will find
instructive and useful guidance here.
This volume is dedicated to Professor Ito on the occasion of his
eightieth birthday as a token of deep appreciation for his great
achievements and contributions. An introduction to and commentary
on the scientific works of Professor Ito are also included.
This book contains three lectures each of 10 sessions; the first on
Potential Theory on graphs and manifolds, the second on annealing
and another algorithms for image reconstruction, the third on
Malliavin Calculus.
Stroock, Daniel W.: Some applications of stochastic calculus to
partial differential equations.- Ikeda, Nobuyuki: Probabilistic
methods in the study of asymptotics.- Nualart, David: Analysis on
Wiener space and anticipating stochastic calculus. "
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