Stochastic and Infinite Dimensional Analysis

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1 Trends in Mathematics Christopher C. Bernido Maria Victoria Carpio-Bernido Martin Grothaus Tobias Kuna Maria João Oliveira José Luís da Silva Editors Stochastic and Infinite Dimensional Analysis

2 Stochastic and Infinite Dimensional Analysis Christopher C. Bernido Maria Victoria Carpio-Bernido Martin Grothaus Tobias Kuna Maria JoQao Oliveira José Luís da Silva Editors

3 Editors Christopher C. Bernido Research Center for Theoretical Physics Central Visayan Institute Foundation Jagna, Bohol, Philippines Martin Grothaus Fachbereich Mathematik Technische Universität Kaiserslautern Kaiserslautern, Germany Maria JoQao Oliveira Universidade Aberta Departamento de Ciências e Tecnologia Lisbon, Portugal Maria Victoria Carpio-Bernido Research Center for Theoretical Physics Central Visayan Institute Foundation Jagna, Bohol, Philippines Tobias Kuna Department of Mathematics and Physics University of Reading Reading, United Kingdom José Luís da Silva Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia Funchal, Madeira, Portugal ISSN ISSN X (electronic) Trends in Mathematics ISBN ISBN (ebook) DOI / Library of Congress Control Number: Mathematics Subject Classification (2010): 60-06, 60HXX, 60H40, 60G22 Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (

4 Contents Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems... 1 Sergio Albeverio Detecting Hierarchical Communities in Networks: A New Approach Michael J. Barber Transition Probabilities for Processes with Memory on Topological Non-trivial Spaces Christopher C. Bernido and M. Victoria Carpio-Bernido Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action Wolfgang Bock Computer Simulations of Self-repelling Fractional Brownian Motion Jinky Bornales, Cresente Cabahug, Roel Baybayon, Sim Bantayan, and Beverly Gemao Principal Solutions Revisited Stephen Clark, Fritz Gesztesy, and Roger Nichols Laplace Operators in Gamma Analysis Dennis Hagedorn, Yuri Kondratiev, Eugene Lytvynov, and Anatoly Vershik 38 Years with Professor Ludwig Streit Takeyuki Hida Quasi-analyticity and Determinacy of the Full Moment Problem from Finite to Infinite Dimensions Maria Infusino ix

5 x Contents Elements for the Retrieval of the Solar Spectrum on the Surface of Mars from an Array of Photodiodes Salvador Jiménez and Luis Vázquez Stochastic Processes on Ends of Tree and Dirichlet Forms Witold Karwowski Completing Canonical Quantization, and Its Role in Nontrivial Scalar Field Quantization John R. Klauder Stochastic Solutions of Nonlinear PDE s and an Extension of Superprocesses Rui Vilela Mendes Maximum Likelihood Drift Estimation for the Mixing of Two Fractional Brownian Motions Yuliya Mishura Existence of Density for Solutions of Mixed Stochastic Equations Taras Shalaiko and Georgiy Shevchenko

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