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Selected Papers
  • Language: en
  • Pages: 648

Selected Papers

  • Type: Book
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  • Published: 1987-01-01
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  • Publisher: Springer

The central and distinguishing feature shared by all the contributions made by K. Ito is the extraordinary insight which they convey. Reading his papers, one should try to picture the intellectual setting in which he was working. At the time when he was a student in Tokyo during the late 1930s, probability theory had only recently entered the age of continuous-time stochastic processes: N. Wiener had accomplished his amazing construction little more than a decade earlier (Wiener, N. , "Differential space," J. Math. Phys. 2, (1923)), Levy had hardly begun the mysterious web he was to eventually weave out of Wiener's P~!hs, the generalizations started by Kolmogorov (Kol mogorov, A. N. , "Uber ...

Essentials of Stochastic Processes
  • Language: en
  • Pages: 192

Essentials of Stochastic Processes

This book is an English translation of Kiyosi Ito's monograph published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areasof the theory of stochastic processes. With the requirements limited to an introductory graduate course on analysis (especially measure theory) and basic probability theory, this book is an excellent text for any g...

On Stochastic Differential Equations
  • Language: en
  • Pages: 64

On Stochastic Differential Equations

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Stochastic Analysis and Related Topics in Kyoto
  • Language: en
  • Pages: 398

Stochastic Analysis and Related Topics in Kyoto

A collection of research and survey papers written by invited lecturers at the RIMS international symposium on stochastic analysis and related topics in celebration of Professor Kiyosi Itt's eighty-eighth birthday. It also covers topics such as quadratic Wiener functionals, representation of martingales, and Itt's construction procedure.

On Stochastic Differential Equations
  • Language: en
  • Pages: 51

On Stochastic Differential Equations

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Itô’s Stochastic Calculus and Probability Theory
  • Language: en
  • Pages: 425

Itô’s Stochastic Calculus and Probability Theory

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. Th...

Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces
  • Language: en
  • Pages: 79

Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces

  • Type: Book
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  • Published: 1984-01-01
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  • Publisher: SIAM

A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.

Diffusion Processes and their Sample Paths
  • Language: en
  • Pages: 341

Diffusion Processes and their Sample Paths

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

Markov Processes from K. Itô's Perspective
  • Language: en
  • Pages: 288

Markov Processes from K. Itô's Perspective

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that desc...

Selected Papers
  • Language: en
  • Pages: 647

Selected Papers

  • Type: Book
  • -
  • Published: 1987
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  • Publisher: Unknown

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