Stochastic and Infinite Dimensional Analysis

Description

This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields. Front Matter....Pages i-x Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems....Pages 1-17 Detecting Hierarchical Communities in Networks: A New Approach....Pages 19-37 Transition Probabilities for Processes with Memory on Topological Non-trivial Spaces....Pages 39-49 Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action....Pages 51-73 Computer Simulations of Self-Repelling Fractional Brownian Motion....Pages 75-84 Principal Solutions Revisited....Pages 85-117 Laplace Operators in Gamma Analysis....Pages 119-147 38 Years with Professor Ludwig Streit....Pages 149-160 Quasi-analyticity and Determinacy of the Full Moment Problem from Finite to Infinite Dimensions....Pages 161-194 Elements for the Retrieval of the Solar Spectrum on the Surface of Mars from an Array of Photodiodes....Pages 195-204 Stochastic Processes on Ends of Tree and Dirichlet Forms....Pages 205-226 Completing Canonical Quantization, and Its Role in Nontrivial Scalar Field Quantization....Pages 227-241 Stochastic Solutions of Nonlinear PDE’s and an Extension of Superprocesses....Pages 243-262 Maximum Likelihood Drift Estimation for the Mixing of Two Fractional Brownian Motions....Pages 263-280 Existence of Density for Solutions of Mixed Stochastic Equations....Pages 281-300