Stochastic Analysis and Applications in Physics

✍ Scribed by Sergio Albeverio, Yuri G. Kondratiev (auth.), Ana Isabel Cardoso, Margarida de Faria, Jürgen Potthoff, Roland Sénéor, Ludwig Streit (eds.)

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Leaves: 454
• Series: NATO ASI Series 449
• Edition: 1
• Category: Library

✦ Synopsis

The intensive exchange between mathematicians and users has led in recent years to a rapid development of stochastic analysis. Of the users, the physicists form perhaps the most important group, giving direction to the mathematicians' research and providing a source of intuition. White noise analysis has emerged as a viable framework for stochastic and infinite dimensional analysis. Another growth area is the theory of stochastic partial differential equations. Gauge field theories are attracting increasing attention. Dirichlet forms provide a fruitful link between the mathematics of Markov processes and the physics of quantum systems. The deterministic--stochastic interface is addressed, as are Euclidean quantum mechanics, excursions of diffusions and the convergence of Markov chains to thermal states.

✦ Table of Contents

Front Matter....Pages i-xv
Infinite Dimensional Diffusions, Markov Fields, Quantum Fields and Stochastic Quantization....Pages 1-34
Burgers Equation Forced by Conservative or Nonconservative Noise....Pages 35-44
Statistical Properties of Piecewise Expanding Maps of the Interval....Pages 45-57
Euclidean Quantum Mechanics. An outline....Pages 59-97
Analysis on Loop Groups....Pages 99-118
White Noise Analysis and Applications....Pages 119-131
Computer Stochastics in Scalar Quantum Field Theory....Pages 133-191
Brownian Motion Over a Kahler Manifold and Elliptic Genera of Level N....Pages 193-217
On Lyapounov Stability Theorems for Stochastic (Deterministic) Evolution Equations 1 ....Pages 219-237
Stochastic Techniques in Condensed Matter Physics....Pages 239-281
Stochastic Partial Differential Equations and Applications to Hydrodynamics....Pages 283-305
White Noise Approach to Parabolic Stochastic Partial Differential Equations....Pages 307-327
Colombeau Generalized Functions and Stochastic Analysis....Pages 329-349
Constructive Field Theoretic Methods and Stochastic Partial Differential Equations....Pages 351-387
Quantum Yang-Mills Theory on Compact Surfaces....Pages 389-403
Entropy and KMS norms....Pages 405-413
An Introduction to White Noise Analysis....Pages 415-439
Excursion Measures for One-Dimensional Time-Homogeneous Diffusions with Inaccessible and Accessible Boundaries....Pages 441-454

✦ Subjects

Probability Theory and Stochastic Processes;Theoretical, Mathematical and Computational Physics;Applications of Mathematics