Stochastic Analysis and Mathematical Physics

An outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Will serve as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics.

Klappentext
Nine survey articles in this volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Key topics covered: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, martingale problem and Markov uniqueness of infinite- dimensional Nelson diffusions, analysis in geometric probability theory, measure-preserving shifts on the Wiener space, cohomology on loop spaces, and stochastic Volterra equations Contributors: H. Airault * L. Coutin * L. Decreusefond * C. Leonard * R. Leandre * P. Lescot * P. Malliavin * M. Oberguggenberger * R. Rebolledo * F. Russo * A.S. Ustunel * L. Wu The work, an outgrowth of a workshop on stochastic analysis held in Lisbon, serves as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, math physics, and physics.

Zusammenfassung
This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.

Inhalt
Functorial Analysis in Geometric Probability Theory.- Stochastic Volterra Equations with Singular Kernels.- Stochastic Diffeology and Homotopy.- Some Results on Entropic Projections.- Mehler-Type Semigroups on Hilbert Spaces and Their Generators.- Singular Limiting Behavior in Nonlinear Stochastic Wave Equations.- Complete Positivity and Open Quantum Systems.- Properties of Measure-preserving Shifts on the Wiener Space.- Martingale and Markov Uniqueness of Infinite Dimensional Nelson Diffusions.

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