Stochastic analysis

✍ Scribed by Kiyosi Ito

• Publisher: NH
• Year: 1985
• Tongue: English
• Leaves: 497
• Series: NHML032
• Category: Library

✦ Synopsis

Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, non-linear functional analysis, control theory and statistical mechanics.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Preface......Page 6
CONTENTS......Page 8
An introduction to Malliavin's calculus......Page 10
Jump processes and boundary processes......Page 62
Diffusive behavior of a random walk in a random medium......Page 114
Random motion of strings and stochastic differential equations on the space C([O, 1], Rc!)......Page 130
An example of a stochastic quantum process: interaction of a quantum particle with a boson field......Page 144
Convergence in L2 of stochastic Ising models: Jump processes and diffusions......Page 158
On the asymptotic behavior of the fundamental solution of the heat equation on certain manifolds......Page 178
Infinite dimensional Ornstein-Uhlenbeck processes......Page 206
Ljapunov indices determine absolutely continuous spectra of stationary random one-dimensional SchrOdinger operators......Page 234
First order stochastic partial differential equations......Page 258
Applications of the Malliavin calculus, Part I......Page 280
Stochastic flows of diffeomorphisms......Page 316
Some recent results in the optimal control of diffusion processes......Page 342
Implicit functions in finite corank on the Wiener Spaces......Page 378
Conditional laws and Hormander's condition......Page 396
Transformations of the Brownian motion on the Lie group......Page 418
Asymptotic behavior of nonlinear Brownian motion near the instability point......Page 432
Entropy functional (free energy) for dynamical systems and their random perturbations......Page 446
Limit theorems for certain diffusion processes with interaction......Page 478