Multidimensional Stochastic Processes As Rough Paths

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Multidimensional Stochastic Processes as Rough Paths

Author : Peter K. Friz
Publisher : Cambridge University Press
ISBN 13 : 1139487213
Total Pages : 671 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Multidimensional Stochastic Processes as Rough Paths by : Peter K. Friz

Download or read book Multidimensional Stochastic Processes as Rough Paths written by Peter K. Friz and published by Cambridge University Press. This book was released on 2010-02-04 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multidimensional Stochastic Processes as Rough Paths

Author : Peter K. Friz
Publisher :
ISBN 13 : 9780511677540
Total Pages : 672 pages
Book Rating : 4.6/5 (775 download)

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Book Synopsis Multidimensional Stochastic Processes as Rough Paths by : Peter K. Friz

Download or read book Multidimensional Stochastic Processes as Rough Paths written by Peter K. Friz and published by . This book was released on 2014-05-14 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers.

A Course on Rough Paths

Author : Peter K. Friz
Publisher : Springer Nature
ISBN 13 : 3030415562
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course on Rough Paths by : Peter K. Friz

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Stochastic Processes with a Multidimensional Parameter

Author : M. Dozzi
Publisher : Longman
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Stochastic Processes with a Multidimensional Parameter by : M. Dozzi

Download or read book Stochastic Processes with a Multidimensional Parameter written by M. Dozzi and published by Longman. This book was released on 1989 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Séminaire de Probabilités XLVI

Author : Catherine Donati-Martin
Publisher : Springer
ISBN 13 : 3319119702
Total Pages : 511 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Séminaire de Probabilités XLVI by : Catherine Donati-Martin

Download or read book Séminaire de Probabilités XLVI written by Catherine Donati-Martin and published by Springer. This book was released on 2014-12-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.

Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics

Author : Wilfried Grecksch
Publisher : World Scientific
ISBN 13 : 9811209804
Total Pages : 261 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics by : Wilfried Grecksch

Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.

Differential Equations Driven by Rough Paths

Author : Terry J. Lyons
Publisher : Springer
ISBN 13 : 3540712852
Total Pages : 126 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Differential Equations Driven by Rough Paths by : Terry J. Lyons

Download or read book Differential Equations Driven by Rough Paths written by Terry J. Lyons and published by Springer. This book was released on 2007-04-25 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths.

New Trends in Stochastic Analysis and Related Topics

Author : Huaizhong Zhao
Publisher : World Scientific
ISBN 13 : 9814360910
Total Pages : 458 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis New Trends in Stochastic Analysis and Related Topics by : Huaizhong Zhao

Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Stochastic and Infinite Dimensional Analysis

Author : Christopher C. Bernido
Publisher : Birkhäuser
ISBN 13 : 3319072455
Total Pages : 304 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Stochastic and Infinite Dimensional Analysis by : Christopher C. Bernido

Download or read book Stochastic and Infinite Dimensional Analysis written by Christopher C. Bernido and published by Birkhäuser. This book was released on 2016-08-10 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Calculus via Regularizations

Author : Francesco Russo
Publisher : Springer Nature
ISBN 13 : 3031094468
Total Pages : 656 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Stochastic Calculus via Regularizations by : Francesco Russo

Download or read book Stochastic Calculus via Regularizations written by Francesco Russo and published by Springer Nature. This book was released on 2022-11-15 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual Itô and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.

Stochastic Analysis and Applications 2014

Author : Dan Crisan
Publisher : Springer
ISBN 13 : 3319112929
Total Pages : 520 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Stochastic Analysis and Applications 2014 by : Dan Crisan

Download or read book Stochastic Analysis and Applications 2014 written by Dan Crisan and published by Springer. This book was released on 2014-12-13 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability and Analysis in Interacting Physical Systems

Author : Peter Friz
Publisher : Springer
ISBN 13 : 303015338X
Total Pages : 294 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Probability and Analysis in Interacting Physical Systems by : Peter Friz

Download or read book Probability and Analysis in Interacting Physical Systems written by Peter Friz and published by Springer. This book was released on 2019-05-24 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15–19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.

Stochastic Integration by Parts and Functional Itô Calculus

Author : Vlad Bally
Publisher : Birkhäuser
ISBN 13 : 3319271288
Total Pages : 213 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Stochastic Integration by Parts and Functional Itô Calculus by : Vlad Bally

Download or read book Stochastic Integration by Parts and Functional Itô Calculus written by Vlad Bally and published by Birkhäuser. This book was released on 2016-03-11 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.

An Introduction to Infinite-Dimensional Differential Geometry

Author : Alexander Schmeding
Publisher : Cambridge University Press
ISBN 13 : 1009089307
Total Pages : 284 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis An Introduction to Infinite-Dimensional Differential Geometry by : Alexander Schmeding

Download or read book An Introduction to Infinite-Dimensional Differential Geometry written by Alexander Schmeding and published by Cambridge University Press. This book was released on 2022-12-22 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

Functional and High-Dimensional Statistics and Related Fields

Author : Germán Aneiros
Publisher : Springer Nature
ISBN 13 : 3030477568
Total Pages : 254 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Functional and High-Dimensional Statistics and Related Fields by : Germán Aneiros

Download or read book Functional and High-Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer Nature. This book was released on 2020-06-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Affine Diffusions and Related Processes: Simulation, Theory and Applications

Author : Aurélien Alfonsi
Publisher : Springer
ISBN 13 : 3319052217
Total Pages : 264 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Affine Diffusions and Related Processes: Simulation, Theory and Applications by : Aurélien Alfonsi

Download or read book Affine Diffusions and Related Processes: Simulation, Theory and Applications written by Aurélien Alfonsi and published by Springer. This book was released on 2015-04-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Partial Differential Equations and Related Fields

Author : Andreas Eberle
Publisher : Springer
ISBN 13 : 3319749293
Total Pages : 565 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Stochastic Partial Differential Equations and Related Fields by : Andreas Eberle

Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.