Approximation Theorems For Levy Driven Marcus Canonical Stochastic Differential Equations

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Approximation Theorems for Lévy-driven Marcus (canonical) Stochastic Differential Equations

Author : Sooppawat Thipyarat
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)

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Book Synopsis Approximation Theorems for Lévy-driven Marcus (canonical) Stochastic Differential Equations by : Sooppawat Thipyarat

Download or read book Approximation Theorems for Lévy-driven Marcus (canonical) Stochastic Differential Equations written by Sooppawat Thipyarat and published by . This book was released on 2024* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider the problem of the numerical approximation of the Marcus (canonical) stochastic differential equations (SDEs) driven by a Brownian motion and an independent the pure jump Lévy process. The numerical scheme used in this thesis is the non-linear discrete time approximation based on the Wong-Zakai approximation scheme. The main results of this thesis are presented in two parts. In the first part, we prove the uniform strong approximation theorem for solutions of the Marcus SDEs. This result is an extension of the approximation results known for Stratonovich SDEs driven by a Brownian motion. We also estimate the convergence rate of strong approximations. The approximation scheme requires the explicit knowledge of the increments of the pure jump Lévy process. In the second part, we apply the method suggested by Asmussen and Rosiński, and approximate the increments of the pure jump Lévy process by a sum of Gaussian and a compound Poisson random variables that can be simulated explicitly. Hence, we examine the weak and strong convergence of the modified Wong-Zakai approximations and also determine the convergence rates. We illustrate our results by a numerical example.

Approximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions

Author : Krystyna Twardowska
Publisher :
ISBN 13 :
Total Pages : 64 pages
Book Rating : 4.3/5 (121 download)

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Book Synopsis Approximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions by : Krystyna Twardowska

Download or read book Approximation Theorems of Wong-Zakai Type for Stochastic Differential Equations in Infinite Dimensions written by Krystyna Twardowska and published by . This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Dynamics of Marcus Type Stochastic Differential Equations

Author : Kai Kümmel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (954 download)

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Book Synopsis On the Dynamics of Marcus Type Stochastic Differential Equations by : Kai Kümmel

Download or read book On the Dynamics of Marcus Type Stochastic Differential Equations written by Kai Kümmel and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Taylor Approximations for Stochastic Partial Differential Equations

Author : Arnulf Jentzen
Publisher : SIAM
ISBN 13 : 9781611972016
Total Pages : 234 pages
Book Rating : 4.9/5 (72 download)

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Book Synopsis Taylor Approximations for Stochastic Partial Differential Equations by : Arnulf Jentzen

Download or read book Taylor Approximations for Stochastic Partial Differential Equations written by Arnulf Jentzen and published by SIAM. This book was released on 2011-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with Hl̲der continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right. The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.

Stochastic Differential Equations

Author : Bernt Øksendal
Publisher : Springer Science & Business Media
ISBN 13 : 3540047581
Total Pages : 406 pages
Book Rating : 4.5/5 (4 download)

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Book Synopsis Stochastic Differential Equations by : Bernt Øksendal

Download or read book Stochastic Differential Equations written by Bernt Øksendal and published by Springer Science & Business Media. This book was released on 2003-07-15 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed in the end of each chapter, in order to facilitate the use of this edition together with previous ones. Several errors have been corrected and formulations have been improved. This has been made possible by the valuable comments from (in alphabetical order) Jon Bohlin, Mark Davis, Helge Holden, Patrick Jaillet, Chen Jing, Natalia Koroleva,MarioLefebvre,Alexander Matasov,Thilo Meyer-Brandis, Keigo Osawa, Bjørn Thunestvedt, Jan Ubøe and Yngve Williassen. I thank them all for helping to improve the book. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the ?gures with great skill. Blindern, September 2002 Bernt Øksendal xv Preface to Corrected Printing, Fifth Edition The main corrections and improvements in this corrected printing are from Chapter 12. I have bene'tted from useful comments from a number of p- ple, including (in alphabetical order) Fredrik Dahl, Simone Deparis, Ulrich Haussmann, Yaozhong Hu, Marianne Huebner, Carl Peter Kirkebø, Ni- lay Kolev, Takashi Kumagai, Shlomo Levental, Geir Magnussen, Anders Øksendal, Jur ̈ gen Pottho?, Colin Rowat, Stig Sandnes, Lones Smith, S- suo Taniguchi and Bjørn Thunestvedt. I want to thank them all for helping me making the book better. I also want to thank Dina Haraldsson for pro'cient typing.

Lectures on Stochastic Differential Equations and Malliavin Calculus

Author : Shinzo Watanabe
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Lectures on Stochastic Differential Equations and Malliavin Calculus by : Shinzo Watanabe

Download or read book Lectures on Stochastic Differential Equations and Malliavin Calculus written by Shinzo Watanabe and published by . This book was released on 1984 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Differential Equations

Author : Bernt Karsten Øksendal
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Stochastic Differential Equations by : Bernt Karsten Øksendal

Download or read book Stochastic Differential Equations written by Bernt Karsten Øksendal and published by Springer Science & Business Media. This book was released on 1998 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this bestselling book introduces the basic theory of stochastic calculus and its applications. Examples are given throughout to illustrate the theory and to show its importance for many applications that arise in areas such as economics, finance, physics, and biology. A new chapter on mathematical finance is included.

Proceedings of the Japan Academy

Author : Nihon Gakushiin
Publisher :
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Proceedings of the Japan Academy by : Nihon Gakushiin

Download or read book Proceedings of the Japan Academy written by Nihon Gakushiin and published by . This book was released on 2001 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Brownian Motion, Martingales, and Stochastic Calculus

Author : Jean-François Le Gall
Publisher : Springer
ISBN 13 : 3319310895
Total Pages : 282 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Brownian Motion, Martingales, and Stochastic Calculus by : Jean-François Le Gall

Download or read book Brownian Motion, Martingales, and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales

Author : P. Protter
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales by : P. Protter

Download or read book Approximations of Solutions of Stochastic Differential Equations Driven by Semimartingales written by P. Protter and published by . This book was released on 1983 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quadrature for Path-dependent Functionals of Lévy-driven Stochastic Differential Equations

Author : Felix Heidenreich
Publisher :
ISBN 13 :
Total Pages : 111 pages
Book Rating : 4.:/5 (849 download)

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Book Synopsis Quadrature for Path-dependent Functionals of Lévy-driven Stochastic Differential Equations by : Felix Heidenreich

Download or read book Quadrature for Path-dependent Functionals of Lévy-driven Stochastic Differential Equations written by Felix Heidenreich and published by . This book was released on 2012 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorial Stochastic Processes

Author : Jim Pitman
Publisher : Springer Science & Business Media
ISBN 13 : 354030990X
Total Pages : 257 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Combinatorial Stochastic Processes by : Jim Pitman

Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

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

Lévy Processes and Stochastic Calculus

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Brownian Motion

Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Brownian Motion by : Peter Mörters

Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Differentiable Measures and the Malliavin Calculus

Author : Vladimir Igorevich Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 082184993X
Total Pages : 506 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differentiable Measures and the Malliavin Calculus by : Vladimir Igorevich Bogachev

Download or read book Differentiable Measures and the Malliavin Calculus written by Vladimir Igorevich Bogachev and published by American Mathematical Soc.. This book was released on 2010-07-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

Stochastic Hybrid Systems

Author : Christos G. Cassandras
Publisher : CRC Press
ISBN 13 : 1420008544
Total Pages : 300 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Stochastic Hybrid Systems by : Christos G. Cassandras

Download or read book Stochastic Hybrid Systems written by Christos G. Cassandras and published by CRC Press. This book was released on 2018-10-03 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.