Stochastic Analysis book cover

Stochastic Analysis

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.

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Published: October 1984

Imprint: North-holland

ISBN: 978-0-444-87588-4

Contents

  • An Introduction to Malliavin's Calculus (N. Ikeda, S. Watanabe). Jump Processes and Boundary Processes (J.M. Bismut). Diffusive Behavior of a Random Walk in a Random Medium (R. Figari, E. Orlandi, G. Papanicolaou). Random Motion of Strings and Stochastic Differential Equations on the Space C ([0,1] Rd) (T. Funaki). An Example of a Stochastic Quantum Process: Interaction of a Quantum Particle with a Boson Field (B. Gaveau). Convergence in L2 of Stochastic Ising Models: Jump Processes and Diffusions (R. Holley). On the Asymptotic Behavior of the Fundamental Solution of the Heat Equation on Certain Manifolds (N. Ikeda). Infinite Dimensional Ornstein-Uhlenbeck Processes (K. Itô). Ljapunov Indices Determine Absolutely Continuous Spectra of Stationary Random One-Dimensional Schrödinger Operators (S. Kotani). First Order Stochastic Partial Differential Equations (H. Kunita). Applications of the Malliavin Calculus, Part I (S. Kusuoka, D. Stroock). Stochastic Flows of Diffeomorphisms (Y. Le Jan and S. Watanabe). Some Recent Results in the Optimal Control of Diffusion Processes (P.L. Lions). Implicit Functions in Finite Corank on the Wiener Space (P. Malliavin). Conditional Laws and Hörmander's Condition (D. Michel). Transformations of the Brownian Motion on the Lie Group (I. Shigekawa). Asymptotic Behavior of Nonlinear Brownian Motion near the Instability Point (M. Suzuki). Entropy Functional (Free Energy) for Dynamical Systems and their Random Perturbations (Y. Takahashi). Limit Theorems for Certain Diffusion Processes with Interaction (H. Tanaka).

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