Multidimensional Stochastic Processes as Rough Paths

Theory and Applications

Author: Peter K. Friz,Nicolas B. Victoir

Publisher: Cambridge University Press

ISBN: 1139487213

Category: Mathematics

Page: N.A

View: 2663

Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.

Affine Diffusions and Related Processes: Simulation, Theory and Applications

Author: Aurélien Alfonsi

Publisher: Springer

ISBN: 3319052217

Category: Mathematics

Page: 252

View: 8671

This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.

Stochastic Analysis and Applications 2014

In Honour of Terry Lyons

Author: Dan Crisan,Ben Hambly,Thaleia Zariphopoulou

Publisher: Springer

ISBN: 3319112929

Category: Mathematics

Page: 503

View: 5125

Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments. It constitutes the proceedings of the conference on "Stochastic Analysis and Applications" held at the University of Oxford and the Oxford-Man Institute during 23-27 September, 2013. The conference honored the 60th birthday of Professor Terry Lyons FLSW FRSE FRS, Wallis Professor of Mathematics, University of Oxford. Terry Lyons is one of the leaders in the field of stochastic analysis. His introduction of the notion of rough paths has revolutionized the field, both in theory and in practice. Stochastic Analysis is the branch of mathematics that deals with the analysis of dynamical systems affected by noise. It emerged as a core area of mathematics in the late 20th century and has subsequently developed into an important theory with a wide range of powerful and novel tools, and with impressive applications within and beyond mathematics. Many systems are profoundly affected by stochastic fluctuations and it is not surprising that the array of applications of Stochastic Analysis is vast and touches on many aspects of life. The present volume is intended for researchers and Ph.D. students in stochastic analysis and its applications, stochastic optimization and financial mathematics, as well as financial engineers and quantitative analysts.

Extraction of Quantifiable Information from Complex Systems

Author: Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant

Publisher: Springer

ISBN: 3319081594

Category: Mathematics

Page: 432

View: 6252

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Splitting Methods in Communication, Imaging, Science, and Engineering

Author: Roland Glowinski,Stanley J. Osher,Wotao Yin

Publisher: Springer

ISBN: 3319415891

Category: Mathematics

Page: 820

View: 7734

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 9465

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Selected Aspects of Fractional Brownian Motion

Author: Ivan Nourdin

Publisher: Springer Science & Business Media

ISBN: 884702823X

Category: Mathematics

Page: 122

View: 302

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

Grundbegriffe der Wahrscheinlichkeitsrechnung

Author: A. Kolomogoroff

Publisher: Springer-Verlag

ISBN: 3642498884

Category: Mathematics

Page: 62

View: 5567

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Operations Research


Author: Frederick S. Hillier,Gerald J. Liebermann

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486792083

Category: Business & Economics

Page: 868

View: 4900

Aus dem Inhalt: Was ist Operations Research? Überblick über die Modellierungsgrundsätze des Operations Research. Einführung in die lineare Programmierung. Die Lösung linearer Programmierungsprobleme: Das Simplexverfahren. Stochastische Prozesse. Warteschlangentheorie. Lagerhaltungstheorie. Prognoseverfahren. Markov-Entscheidungsprozesse. Reliabilität. Entscheidungstheorie. Die Theorie des Simplexverfahrens Qualitätstheorie und Sensitivitätsanalyse Spezialfälle linearer Programmierungsprobleme. Die Formulierung linearer Programmierungsmodelle und Goal-Programmierung. Weitere Algorithmen der linearen Programmierung. Netzwerkanalyse einschließlich PERT-CPM. Dynamische Optimierung. Spieltheorie. Ganzzahlige Programmierung. Nichtlineare Programmierung Simulation. Anhang. Lösungen für ausgewählte Übungsaufgaben.

Partielle Differentialgleichungen

Elliptische (und parabolische) Gleichungen

Author: Jürgen Jost

Publisher: Springer-Verlag

ISBN: 3642588883

Category: Mathematics

Page: 291

View: 1963

Dieses Lehrbuch bietet eine Einführung in die moderne Theorie der partiellen Differentialgleichungen. Der Leser wird zu den wichtigen Methoden und den wesentlichen Aussagen in diesem Bereich hingeführt, wobei der Schwerpunkt auf den elliptischen partiellen Differentialgleichungen liegt. Ausgehend von der Laplace-Gleichung (harmonische Funktionen) entwickelt der Autor systematische Techniken, die auch auf größere Klassen von Differentialgleichungen, und hier insbesondere auch auf nichtlineare Differentialgleichungen, anwendbar sind. Zur Veranschaulichung wurden zahlreiche Übungsaufgaben aufgenommen. Das Buch richtet sich vor allem an Studenten der Mathematik im Hauptstudium, kann aber für interessierte Studenten auch gegebenenfalls schon ab dem dritten Semester verwendet werden.

Data mining

praktische Werkzeuge und Techniken für das maschinelle Lernen

Author: Ian H. Witten,Eibe Frank

Publisher: N.A

ISBN: 9783446215337


Page: 386

View: 1337

Grounded theory

Strategien qualitativer Forschung

Author: Barney G. Glaser,Anselm L. Strauss,Axel T. Paul

Publisher: N.A

ISBN: 9783456849065


Page: 278

View: 776

Der Klassiker über den qualitativen Forschungsansatz der "Grounded Theory", geschrieben von den Entwicklern dieser Methode "Obwohl unser Buch sich in erster Linie an Soziologen richtet, glauben wir, dass es jedem nutzen kann, der daran interessiert ist, soziale Phänomene zu untersuchen politischer, pädagogischer, wirtschaftlicher, industrieller oder welcher Art auch immer." In der Tat ist "Grounded Theory" quer durch die wissenschaftlichen Disziplinen zum Standardbegriff der qualitativen Sozialforschung ge - worden. Die inzwischen zum Klassiker avancierte Arbeit von Glaser und Strauss eröffnet eine lehrbare und auch lernbare Forschungsstrategie. Das Konzept bietet eine Antwort auf das Problem, die oft schmerzlich empfundene Lücke zwischen empirischer Forschung und Theorie zu schliessen.

Finite Elemente

Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie

Author: Dietrich Braess

Publisher: Springer-Verlag

ISBN: 3662072335

Category: Technology & Engineering

Page: 320

View: 1024

Diese völlig überarbeitete Neuauflage bietet dem Leser eine gründliche Einführung in die Methode der Finiten Elemente, welche heute verstärkt zur numerischen Lösung von partiellen Differentialgleichungen eingesetzt werden. Die Theorie wird so weit entwickelt, daß der Leser mit Kenntnissen aus den Grundvorlesungen des Mathematikstudiums auskommt. Dem für die Praxis relevanten Mehrgitterverfahren und der Methode der konjugierten Gradienten wird ein breiter Platz eingeräumt. Ausführlich wird die Strukturmechanik als ein wichtiger und typischer Anwendungsbereich für Finite Elemente behandelt. Da dieser Aspekt in anderen Lehrbüchern kaum Berücksichtigung findet, wurde er in der Neuauflage stark überarbeitet und abgerundet. Als weitere Ergänzung ist vor allem die Diskussion von a posteriori Schätzern zu nennen.


Deterministische Beobachtung und stochastische Filterung

Author: Karl Brammer,Gerhard Siffling

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486785524

Category: Science

Page: 232

View: 5460

Das Buch führt den Leser auf elementarem Wege in die Wahrscheinlichkeitsrechnung und in die Theorie der Zufallsprozesse ein, wobei keinerlei Vorkenntnisse auf diesem Gebiet vorausgesetzt werden. Schließlich wird gezeigt, wie sich die Eigenschaften eines Zufallsprozesses bei der Übertragung durch ein lineares System verändern und wie diese veränderten Eigenschaften berechnet werden können.