Stochastic and Infinite Dimensional Analysis (Trends in Mathematics)

by Christopher Bernido (Editor), Maria Victoria Carpio-Bernido (Editor), Martin Grothaus (Editor), Tobias Kuna (Editor), Maria João Oliveira (Editor), José Luís da Silva (Editor)



Features scientific contributions by world leading experts in the fields of systems of infinite degrees of freedom

Prominent presentation of the different guises of these fields such as infinite dimensional analysis, stochastic processes and white noise analysis

Ties together papers treating applications of systems of infinitely many degrees of freedom ranging from martian atmosphere to social networks in a rather unique way rarely to be found in single publications of this kind

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.

Table of contents (15 chapters)

Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems

Detecting Hierarchical Communities in Networks: A New Approach

Transition Probabilities for Processes with Memory on Topological Non-trivial Spaces

Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action

Computer Simulations of Self-Repelling Fractional Brownian Motion

Principal Solutions Revisited

Laplace Operators in Gamma Analysis

38 Years with Professor Ludwig Streit

Quasi-analyticity and Determinacy of the Full Moment Problem from Finite to Infinite Dimensions

Elements for the Retrieval of the Solar Spectrum on the Surface of Mars from an Array of Photodiodes

Stochastic Processes on Ends of Tree and Dirichlet Forms

Completing Canonical Quantization, and Its Role in Nontrivial Scalar Field Quantization

Stochastic Solutions of Nonlinear PDE’s and an Extension of Superprocesses

Maximum Likelihood Drift Estimation for the Mixing of Two Fractional Brownian Motions

Existence of Density for Solutions of Mixed Stochastic Equations