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Stochastic Calculus of Variations in Mathematical Finance

Stochastic Calculus of Variations in Mathematical Finance Author Paul Malliavin
ISBN-10 9783540307990
Release 2006-02-25
Pages 142
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Highly esteemed author Topics covered are relevant and timely



Stochastic Calculus of Variations for Jump Processes

Stochastic Calculus of Variations for Jump Processes Author Yasushi Ishikawa
ISBN-10 9783110282009
Release 2013-05-28
Pages 274
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This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book processes "with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Up to now, these topics were rarely discussed in a monograph.



Stochastic Calculus of Variations

Stochastic Calculus of Variations Author Yasushi Ishikawa
ISBN-10 9783110392326
Release 2016-03-07
Pages 288
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This monograph is a concise introduction to the stochastic calculus of variations for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. The author provides many results on this topic in a self-contained way. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance.



Stochastic Analysis and Applications

Stochastic Analysis and Applications Author I M Davies
ISBN-10 9789814548113
Release 1996-03-20
Pages 520
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This volume contains papers which were presented at a meeting entitled “Stochastic Analysis and Applications“ held at Gregynog Hall, Powys, from the 9th — 14th July 1995. The meeting consisted of a mixture of plenary/review talks and special interest sessions covering most of the current areas of activity in stochastic analysis. The meeting was jointly organized by the Department of Mathematics, University of Wales Swansea and the Mathematics Institute, University of Warwick in connection with the Stochastic Analysis year of activity. The papers contained herein are accessible to workers in the field of stochastic analysis and give a good coverage of topics of current interest in the research community. Contents:Logarithmic Sobolev Inequalities on Loop Spaces Over Compact Riemannian Manifolds (S Aida)Euclidean Random Fields, Pseudodifferential Operators, and Wightman Functions (S Albeverio et al)Strong Markov Processes and the Dirichlet Problem in von Neumann Algebras (S Attal & K R Parthasarathy)On the General Form of Quantum Stochastic Evolution Equation (V P Belavkin)Stochastic Flows of Diffeomorphisms (Z Brzezniak & K D Elworthy)Gromov's Hyperbolicity and Picard's Little Theorem for Harmonic Maps (M Cranston et al)On Heat Kernel Logarithmic Sobolev inequalities (B K Driver & Y Hu)Evolution Equations in the Theory of Statistical Manifolds (B Grigelionis)Stochastic Flows with Self-Similar Properties (H Kunita)Path Space of a Symplectic Manifold (R Léandre)The General Linear Stochastic Volterra Equation with Anticipating Coefficients (B Øksendal & T Zhang)Local Non Smooth Flows on the Wiener Space and Applications (G Peters)On Transformations of Measures Related to Second Order Differential Equations (V R Steblovskaya)Extension of Lipschitz Functions on Wiener Space (A S Üstünel & M Zakai)On Large Deviations for SDE Systems Without Bounded Coefficient Derivatives (A Y Veretennikov)Maupertius' Least Action Principle for Diffusions (J C Zambrini)Large Deviations Results Without Continuity Hypothesis on the Diffusion Term (W Zheng)and other papers Readership: Stochastic analysts, mathematical physicists and probabilists. keywords:



Analysis of Variations for Self similar Processes

Analysis of Variations for Self similar Processes Author Ciprian A. Tudor
ISBN-10 9783319009360
Release 2013-08-13
Pages 268
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Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.



Malliavin Calculus and Stochastic Analysis

Malliavin Calculus and Stochastic Analysis Author Frederi Viens
ISBN-10 9781461459064
Release 2013-02-15
Pages 583
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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.



The Malliavin Calculus

The Malliavin Calculus Author Denis R. Bell
ISBN-10 9780486152059
Release 2012-12-03
Pages 128
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This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.



The Malliavin Calculus and Related Topics

The Malliavin Calculus and Related Topics Author David Nualart
ISBN-10 9783540283294
Release 2006-02-27
Pages 382
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The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.



The Malliavin Calculus and Related Topics

The Malliavin Calculus and Related Topics Author David Nualart
ISBN-10 9783540283294
Release 2006-02-27
Pages 382
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The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.



Functional Analysis Calculus of Variations and Optimal Control

Functional Analysis  Calculus of Variations and Optimal Control Author Francis Clarke
ISBN-10 9781447148203
Release 2013-02-06
Pages 591
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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.



Integration and Probability

Integration and Probability Author Paul Malliavin
ISBN-10 9781461242024
Release 2012-12-06
Pages 326
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An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.



Malliavin Calculus for L vy Processes with Applications to Finance

Malliavin Calculus for L  vy Processes with Applications to Finance Author Giulia Di Nunno
ISBN-10 3540785728
Release 2008-10-08
Pages 418
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This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.



Introduction to Stochastic Analysis and Malliavin Calculus

Introduction to Stochastic Analysis and Malliavin Calculus Author Jai Rathod
ISBN-10 1681171902
Release 2015-08-01
Pages 228
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Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The Malliavin calculus extends the calculus of variations from functions to stochastic processes. The Malliavin calculus is also called the stochastic calculus of variations. In particular, it allows the computation of derivatives of random variables. Malliavin's ideas led to a proof that Hörmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications in, for example, stochastic filtering. This book emphasizes on differential stochastic equations and Malliavin calculus.



Dynamic Optimization Second Edition

Dynamic Optimization  Second Edition Author Morton I. Kamien
ISBN-10 9780486310282
Release 2013-04-17
Pages 400
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Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.



Large deviations and the Malliavin calculus

Large deviations and the Malliavin calculus Author Jean-Michel Bismut
ISBN-10 0817632204
Release 1984-04-06
Pages 216
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Large deviations and the Malliavin calculus has been writing in one form or another for most of life. You can find so many inspiration from Large deviations and the Malliavin calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Large deviations and the Malliavin calculus book for free.



Probability Theory III

Probability Theory III Author Alʹbert Nikolaevich Shiri͡aev
ISBN-10 3540546871
Release 1998
Pages 253
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Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t.



L vy Processes and Stochastic Calculus

L  vy Processes and Stochastic Calculus Author CTI Reviews
ISBN-10 9781467205108
Release 2016-10-16
Pages 29
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Facts101 is your complete guide to Lèvy Processes and Stochastic Calculus. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.