Proceedings of the International Conference on Stochastic Analysis and Applications: Hammamet, 2001 / Edition 1

by Sergio Albeverio, Anne Boutet de Monvel, Habib Ouerdiane

Overview

Shastic analysis is a field of mathematical research having numerous interactions with other domains of mathematics such as partial differential equations, riemannian path spaces, dynamical systems, optimization. It also has many links with applications in engineering, finance, quantum physics, and other fields. This book covers recent and diverse aspects of shastic and infinite-dimensional analysis. The included papers are written from a variety of standpoints (white noise analysis, Malliavin calculus, quantum shastic calculus) by the contributors, and provide a broad coverage of the subject.

This volume will be useful to graduate students and research mathematicians wishing to get acquainted with recent developments in the field of shastic analysis.

Product Details

ISBN-13:	9781402024672
Publisher:	Springer Netherlands
Publication date:	08/10/2004
Edition description:	2004
Pages:	350
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Mathematical aspects of decoherence induced classicality in quantum systems.- Hankel operators on Segal-Bargmann spaces.- Malliavin calculus and real Bott periodicity.- Heat equation associated with Lévy laplacian.- Zeta-regularized traces versus the Wodzicki residue as tools in quantum field theory and infinite dimensional geometry.- Quantum shastic calculus applied to path spaces over Lie groups.- Martingale approximation for self-intersection local time of brownian motion.- Itô formula for generalized functionals of brownian bridge.- Fock space operator valued martingale convergence.- Shastic integration for compensated Poisson measures and the Lévy-Itô formula.- Exponential ergodicity of classical and quantum Markov birth and death semigroups.- Asymptotic flux across hypersurfaces for diffusion processes.- Reflected backward shastic differential equation with superlinear growth.- Semidynamical systems with the same order relation.- Infinite-dimensional Lagrange problem and application to shastic processes.- On portfolio separation in the Merton problem with bankruptcy or default.- Square of white noise unitary evolutions on boson Fock space.- Numerical solution of Wick shastic differential equations.