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Stochastic Integration With Jumps

Author: Klaus Bichteler
Publisher: Cambridge University Press
ISBN: 9780521811293
Size: 51.66 MB
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The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.

Stochastic Integration Theory

Author: Peter Medvegyev
Publisher: Oxford University Press on Demand
ISBN: 0199215251
Size: 76.46 MB
Format: PDF
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This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownianmotion, Poisson process).

Stochastic Calculus For Quantitative Finance

Author: Alexander A Gushchin
Publisher: Elsevier
ISBN: 0081004761
Size: 59.37 MB
Format: PDF, ePub
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In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance

Stochastic Calculus Of Variations

Author: Yasushi Ishikawa
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110378078
Size: 25.81 MB
Format: PDF, Docs
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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.

Yosida Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications

Author: T.E. Govindan
Publisher: Springer
ISBN: 3319456849
Size: 75.88 MB
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This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.

Multiple Scattering

Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 0521865549
Size: 54.44 MB
Format: PDF, Kindle
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First book devoted to subject; an essential reference for applied mathematicians, physicists and engineers.

Integration A Functional Approach

Author: Klaus Bichteler
Publisher: Springer Science & Business Media
ISBN: 303480055X
Size: 44.38 MB
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This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.