| Stochastic Calculus of Variations Contributor(s): Ishikawa, Yasushi (Author) |
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ISBN: 3110377764 ISBN-13: 9783110377767 Publisher: de Gruyter OUR PRICE: $217.80 Product Type: Hardcover - Other Formats Published: March 2016 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - Stochastic Processes - Mathematics | Mathematical Analysis - Mathematics | Differential Equations - General |
| Dewey: 519.22 |
| LCCN: 2016012640 |
| Series: de Gruyter Studies in Mathematics |
| Physical Information: 0.69" H x 6.69" W x 9.61" (1.46 lbs) 288 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener-Poisson space. Solving the Hamilton-Jacobi-Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory.The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: PrefacePreface to the second editionIntroductionLévy processes and Itô calculusPerturbations and properties of the probability lawAnalysis of Wiener-Poisson functionalsApplicationsAppendixBibliographyList of symbolsIndex |
Contributor Bio(s): Ishikawa, Yasushi: - Yasushi Ishikawa, Ehime University, Matsuyama, Japan. |