Download or read book Fractional Stochastic Calculus Via Stochastic Sewing written by Toyomu Matsuda and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Models for Fractional Calculus written by Mark M. Meerschaert and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.

Download or read book Stochastic Calculus for Fractional Brownian Motion and Related Processes written by Yuliya Mishura and published by Springer. This book was released on 2008-04-12 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

Download or read book Stochastic Calculus Via Regularizations written by Francesco Russo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Calculus for Fractional Brownian Motion and Related Processes written by Yuliya S. Mishura and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0

Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.

Download or read book An Introduction to Stochastic Integration written by Kai L. Chung and published by Birkhäuser Boston. This book was released on 1990-01-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Integration by Parts and Functional It 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.

Download or read book Stochastic Calculus with Respect to Fractional Brownian Motion with Hurst Parameter Less Than 1 2 written by Elisa Alòs and published by . This book was released on 1999 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stratonovich Stochastic Calculus for Fractional Brownian Motion with Hurst Parameter Lesser Than 1 2 written by E. Alòs and published by . This book was released on 2000 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recent Advances in Stochastic Calculus written by John S. Baras and published by . This book was released on 1990 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Integrals written by Heinrich von Weizsäcker and published by Springer-Verlag. This book was released on 2013-07-02 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Stochastic Analysis and Malliavin Calculus written by Giuseppe Da Prato and published by Springer. This book was released on 2008 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown from a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with the differential stochastic equations and their connection with parabolic problems. The third part contains an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems.

Download or read book The Application of Fractional Calculus to the Simulation of Stochastic Processes written by Frank B. Tatom and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebane and published by . This book was released on 1998 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Informal Introduction to Stochastic Calculus with Applications written by Ovidiu Calin and published by World Scientific Publishing Company. This book was released on 2021-11-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory. The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus. The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods. This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises. This edition has also improved presentation from the first edition in several chapters, including new material.

Download or read book Seminar on Stochastic Analysis Random Fields and Applications written by Robert C. Dalang and published by . This book was released on 1999 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: