Stokastik

Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum fieldtheory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.

"The Art of Randomness teaches readers to harness the power of randomness (and Python code) to solve real-world problems in programming, science, and art through hands-on experiments-from simulating evolution to encrypting messages to making machine-learning algorithms. Each chapter describes how randomness plays into the given topic area, then proceeds to demonstrate its problem-solving role with hands-on experiments to work through using Python code"--

The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.

in die Statistik 5., durchgesehene Auflage Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet uber abrufbar. Prof. Dr. rer. nat. Jurgen Lehn Geboren 1941 in Karlsruhe. Studium der Mathematik an den Universitaten Karlsruhe und Regensburg. 1968 Diplom in Karlsruhe, 1972 Promotion in Regensburg, 1978 Habilitation in Karlsruhe. 1978 Professor an der Technischen Hochschule Darmstadt. Prof. Dr. rer. nat. Helmut Wegmann Geboren 1938 in Worms. Studium der Mathematik und Physik an den Universitaten Mainz und Tubingen. Wiss. Assistent an den Universitaten Mainz und Stuttgart. 1962 Staats- amen in Mainz, 1964 Promotion in Mainz, 1969 Habilitation in Stuttgart. 1970 Professor fur Mathematik an der Technischen Hochschule Darmstadt. 1. Auflage 1985 2. Auflage 1992 3. Auflage 2000 4. Auflage 2004 5., durchgesehene Auflage Juni 2006 Alle Rechte vorbehalten (c) B.G.Teubner Verlag / GWV Fachverlage GmbH, Wiesbaden 2006 Lektorat: Ulrich Sandten / Kerstin Hoffmann Der B. G. Teubner Verlag ist ein Unternehmen von Springer Science+Business Media. www.teubner.de Das Werk einschlielich aller seiner Teile ist urheberrechtlich geschutzt. Jede Verwertung auerhalb der engen Grenzen des Urheberrech- gesetzes ist ohne Zustimmung des Verlags unzulassig und strafbar. Das gilt insbesondere fur Vervielfaltigungen, Ubersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen.

This book introduces the advances in synchromodal logistics and provides a framework to classify various optimisation problems in this field. It explores the application of this framework to solve a broad range of problems, such as problems with and without a central decision-maker, problems with and without full information, deterministic problems, problems coping with uncertainty, optimisation of a full network design problem. It covers theoretical constructs, such as discrete optimisation, robust optimisation, optimisation under uncertainty, multi-objective optimisation and agent based equilibrium models. Moreover, practical elaborated use cases are presented to deepen understanding. The book gives both researchers and practitioners a good overview of the field of synchromodal optimisation problems and offers the reader practical methods for modelling and problem-solving.

This book addresses the problem of multi-agent systems, considering that it can be interpreted as a generalized multi-synchronization problem. From manufacturing tasks, through encryption and communication algorithms, to high-precision experiments, the simultaneous cooperation between multiple systems or agents is essential to successfully carrying out different modern activities, both in academy and industry. For example, the coordination of multiple assembler robots in manufacturing lines. These agents need to synchronize.The first two chapters of the book describe the synchronization of dynamical systems, paying special attention to the synchronization of non-identical systems. Following, the third chapter presents an interesting application of the synchronization phenomenon for state estimation. Subsequently, the authors fully address the multi-agent problem interpreted as multi-synchronization. The final chapters introduce the reader to a more complex problem, the synchronization of systems governed by partial differential equations, both of integer and fractional order.The book aimed at graduates, postgraduate students and researchers closely related to the area of automatic control. Previous knowledge of linear algebra, classical and fractional calculus is requested, as well as some fundamental notions of graph theory.

This book helps readers easily learn basic model checking by presenting examples, exercises and case studies. The toolset mCRL2 provides a language to specify the behaviour of distributed systems, in particular where there is concurrency with inter-process communication. This language allows us to analyse a distributed system with respect to its functional requirements. For example, biological cells, supply chain management systems, patient support platforms, and communication protocols.The underlying technique is based on verifying requirements through model checking. The book explains the syntax of mCRL2 and offers modelling tips and tricks.

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician.Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader¿s intuition.By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation.Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

This book is a rigorous but practical presentation of the techniques of uncertainty quantification, with applications in R and Python. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R and Python allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi-objective optimization, game theory, as well as linear algebraic equations, and probability and statistics. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.

This book aims to clarify the priorities of the Sendai Framework for the DRR 2015 - 2030, through gathering recent contributions addressing the different ways researchers define, measure, reduce, and manage risk in the challenge of the DRR. Beyond a discussion of the different definitions of disaster risk; this book provides contributions focused on optimization approaches that support the decision-making process in the challenge of managing DRR problems considering emerging disaster risks in the medium and long term, as well as national and local applications. Some of the topics covered include network flow problems, stochastic optimization, discrete optimization, multi-objective programming, approximation techniques, and heuristic approaches.The target audience of the book includes professionals who work in Linear Programming, Logistics, Optimization (Mathematical, Robust, Stochastic), Management Science, Mathematical Programming, Networks, Scheduling, Simulation, Supply Chain Management, Sustainability, and similar areas. It can be useful for researchers, academics, graduate students, and anyone else doing research in the field

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications.The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications.                                                                                                       The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie's Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

This text provides a concise introduction, suitable for a one-semester special topicscourse, to the remarkable properties of Gaussian measures on both finite and infinitedimensional spaces. It begins with a brief resumé of probabilistic results in which Fourieranalysis plays an essential role, and those results are then applied to derive a few basicfacts about Gaussian measures on finite dimensional spaces. In anticipation of the analysisof Gaussian measures on infinite dimensional spaces, particular attention is given to thoseproperties of Gaussian measures that are dimension independent, and Gaussian processesare constructed. The rest of the book is devoted to the study of Gaussian measures onBanach spaces. The perspective adopted is the one introduced by I. Segal and developedby L. Gross in which the Hilbert structure underlying the measure is emphasized.The contents of this bookshould be accessible to either undergraduate or graduatestudents who are interested in probability theory and have a solid background in Lebesgueintegration theory and a familiarity with basic functional analysis. Although the focus ison Gaussian measures, the book introduces its readers to techniques and ideas that haveapplications in other contexts.

Dieses Buch ist die erste fachübergreifende Einführung in die Kombinatorik in deutscher Sprache und umfasst Gesetzmäßigkeiten, Rechenregeln, Anwendungen sowie 50 Übungsaufgaben mit Lösungen. Es zeigt, wie dieses oft unterschätzte Fachgebiet zahlreiche Entwicklungen in Linguistik und Lyrik, Mathematik und Informatik, Chemie, Musik, Psychologie, Soziologie und Ökonomie beeinflusste.

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes - Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include Matlab computations, and the numerous end-of-chapter exercises include computational assignments. Matlab code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.