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

Stochastic 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 stochastic and infinite-dimensional analysis. The included papers are written from a variety of standpoints (white noise analysis, Malliavin calculus, quantum stochastic 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 stochastic analysis. Front Matter....Pages i-ix Mathematical Aspects of Decoherence Induced Classicality in Quantum Systems....Pages 1-15 Hankel Operators on Segal-Bargmann Spaces....Pages 17-36 Malliavin Calculus and Real Bott Periodicity....Pages 37-51 Heat Equation Associated with Lévy Laplacian....Pages 53-68 Zeta-Regularized Traces Versus the Wodzicki Residue as Tools in Quantum Field Theory and Infinite Dimensional Geometry....Pages 69-84 Quantum Stochastic Calculus Applied to Path Spaces over Lie Groups....Pages 85-94 Martingale Approximation for Self-Intersection Local Time of Brownian Motion....Pages 95-106 Itô Formula for Generalized Functionals of Brownian Bridge....Pages 107-127 Fock Space Operator Valued Martingale Convergence....Pages 129-143 Stochastic Integration for Compensated Poisson Measures and the Lévy-Itô Formula....Pages 145-167 Exponential Ergodicity of Classical and Quantum Markov Birth and Death Semigroups....Pages 169-183 Asymptotic Flux Across Hypersurfaces for Diffusion Processes....Pages 185-197 Reflected Backward Stochastic Differential Equation with Super-Linear Growth....Pages 199-216 Semidynamical Systems with the Same Order Relation....Pages 217-237 Infinite-Dimensional Lagrange Problem and Application to Stochastic Processes....Pages 239-248 On Portfolio Separation in the Merton Problem with Bankruptcy or Default....Pages 249-265 Square of White Noise Unitary Evolutions on Boson Fock Space....Pages 267-301 Numerical Solution of Wick-Stochastic Partial Differential Equations....Pages 303-349

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.