Ebook: 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. 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.

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Content:
Front Matter....Pages i-xiv
L?vy measure of superprocesses; absorption processes....Pages 1-14
A class of integration by parts formulae in stochastic analysis I....Pages 15-30
Smooth measures and continuous additive functionals of right Markov processes....Pages 31-49
On decomposition of additive functionals of reflecting Brownian motions....Pages 51-61
Equilibrium fluctuations for lattice gas....Pages 63-72
Hall’s transform and the Segal-Bargmann map....Pages 73-116
Lagrangian for pinned diffusion process....Pages 117-128
Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion....Pages 129-139
Van Vleck-Pauli formula for Wiener integrals and Jacobi fields....Pages 141-156
Some recent developments in nonlinear filtering theory....Pages 157-170
Detecting a single defect in a scenery by observing the scenery along a random walk path....Pages 171-183
Analytic approach to Yor’s formula of exponential additive functionals of Brownian motion....Pages 185-195
Stochastic differential equations with jumps and stochastic flows of diffeomorphisms....Pages 197-211
A Remark on American Securities....Pages 213-231
Calculus for multiplicative functionals, It?’s formula and differential equations....Pages 233-250
A Martin boundary connected with the ?-volume limit of the focussing cubic Schr?dinger equation....Pages 251-259
Diffusion processes on an open time interval and their time reversal....Pages 261-280
On sensitive control and differential games in infinite dimensional spaces....Pages 281-292
Decomposition at the maximum for excursions and bridges of one-dimensional diffusions....Pages 293-310
A K?hler metric on a based loop group and a covariant differentiation....Pages 311-326
Burgers system driven by a periodic stochastic flow....Pages 327-346
An estimate on the Hessian of the heat kernel....Pages 347-353
Environment-wise central limit theorem for a diffusion in a Brownian environment with large drift....Pages 355-371
The complex story of simple exclusion....Pages 373-384
L?vy’s stochastic area formula and Brownian motion on compact Lie groups....Pages 385-400
Principal values of Brownian local times and their related topics....Pages 401-411
....Pages 413-422