Stochastic Calculus Via Regularizations
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Stochastic Calculus Via Regularizations
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Author : Francesco Russo
language : en
Publisher: Springer Nature
Release Date : 2022-11-15
Stochastic Calculus Via Regularizations written by Francesco Russo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-15 with Mathematics categories.
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.
Probability On Algebraic And Geometric Structures
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Author : Gregory Budzban
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-29
Probability On Algebraic And Geometric Structures written by Gregory Budzban and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-29 with Mathematics categories.
This volume contains the proceedings of the International Research Conference “Probability on Algebraic and Geometric Structures”, held from June 5–7, 2014, at Southern Illinois University, Carbondale, IL, celebrating the careers of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea. These proceedings include survey papers and new research on a variety of topics such as probability measures and the behavior of stochastic processes on groups, semigroups, and Clifford algebras; algebraic methods for analyzing Markov chains and products of random matrices; stochastic integrals and stochastic ordinary, partial, and functional differential equations.
Stochastics Of Environmental And Financial Economics
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Author : Fred Espen Benth
language : en
Publisher: Springer
Release Date : 2015-10-23
Stochastics Of Environmental And Financial Economics written by Fred Espen Benth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Science categories.
These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.
S Minaire De Probabilit S Xl
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Author : Catherine Donati-Martin
language : en
Publisher: Springer
Release Date : 2007-07-25
S Minaire De Probabilit S Xl written by Catherine Donati-Martin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-25 with Mathematics categories.
Who could have predicted that the S ́ eminaire de Probabilit ́ es would reach the age of 40? This long life is ?rst due to the vitality of the French probabil- tic school, for which the S ́ eminaire remains one of the most speci?c media of exchange. Another factor is the amount of enthusiasm, energy and time invested year after year by the R ́ edacteurs: Michel Ledoux dedicated himself tothistaskuptoVolumeXXXVIII,andMarcYormadehisnameinseparable from the S ́ eminaire by devoting himself to it during a quarter of a century. Browsing among the past volumes can only give a faint glimpse of how much is owed to them; keeping up with the standard they have set is a challenge to the new R ́ edaction. In a changing world where the status of paper and ink is questioned and where, alas, pressure for publishing is increasing, in particular among young mathematicians, we shall try and keep the same direction. Although most contributions are anonymously refereed, the S ́ eminaire is not a mathema- cal journal; our ?rst criterion is not mathematical depth, but usefulness to the French and international probabilistic community. We do not insist that everything published in these volumes should have reached its ?nal form or be original, and acceptance–rejection may not be decided on purely scienti?c grounds.
Non Gaussian Selfsimilar Stochastic Processes
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Author : Ciprian Tudor
language : en
Publisher: Springer Nature
Release Date : 2023-07-04
Non Gaussian Selfsimilar Stochastic Processes written by Ciprian Tudor and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-04 with Mathematics categories.
This book offers an introduction to the field of stochastic analysis of Hermite processes. These selfsimilar stochastic processes with stationary increments live in a Wiener chaos and include the fractional Brownian motion, the only Gaussian process in this class. Using the Wiener chaos theory and multiple stochastic integrals, the book covers the main properties of Hermite processes and their multiparameter counterparts, the Hermite sheets. It delves into the probability distribution of these stochastic processes and their sample paths, while also presenting the basics of stochastic integration theory with respect to Hermite processes and sheets. The book goes beyond theory and provides a thorough analysis of physical models driven by Hermite noise, including the Hermite Ornstein-Uhlenbeck process and the solution to the stochastic heat equation driven by such a random perturbation. Moreover, it explores up-to-date topics central to current research in statistical inference for Hermite-driven models.
Stochastic Partial Differential Equations And Related Fields
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Author : Andreas Eberle
language : en
Publisher: Springer
Release Date : 2018-07-03
Stochastic Partial Differential Equations And Related Fields written by Andreas Eberle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Mathematics categories.
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.
Malliavin Calculus And Stochastic Analysis
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Author : Frederi Viens
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-15
Malliavin Calculus And Stochastic Analysis written by Frederi Viens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-15 with Mathematics categories.
The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.
Singular Random Dynamics
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Author : Massimiliano Gubinelli
language : en
Publisher: Springer Nature
Release Date : 2019-11-12
Singular Random Dynamics written by Massimiliano Gubinelli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-12 with Mathematics categories.
Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton–Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of regularity structures and related theories, with the KPZ equation as a central example; and the study of dispersive equations with random initial conditions, which gives new insights into classical problems and at the same time provides a surprising parallel to the theory of singular SPDEs, viewed from many different perspectives. These notes are aimed at graduate students and researchers who want to familiarize themselves with this new field, which lies at the interface between analysis and probability.
Theory Of Stochastic Integrals
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Author : Jorge A. León
language : en
Publisher: CRC Press
Release Date : 2025-03-14
Theory Of Stochastic Integrals written by Jorge A. León and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.
In applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Itô theory. It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations. Theory of Stochastic Integrals aims to provide the answer to this problem by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales, such as Volterra Gaussian processes, or processes with bounded p-variation among which we can mention fractional Brownian motion and Riemann-Liouville fractional process. Features Self-contained treatment of the topic Suitable as a teaching or research tool for those interested in stochastic analysis and its applications Includes original results.
Modern Stochastics And Applications
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Author : Volodymyr Korolyuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-30
Modern Stochastics And Applications written by Volodymyr Korolyuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-30 with Mathematics categories.
This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.