Stochastic Calculus of Variations : : For Jump Processes / / Yasushi Ishikawa.
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"...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2016] ©2016 |
Year of Publication: | 2016 |
Edition: | 2nd ed. |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
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Physical Description: | 1 online resource (278 p.) |
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Ishikawa, Yasushi, author. aut http://id.loc.gov/vocabulary/relators/aut Stochastic Calculus of Variations : For Jump Processes / Yasushi Ishikawa. 2nd ed. Berlin ; Boston : De Gruyter, [2016] ©2016 1 online resource (278 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 54 Frontmatter -- Preface -- Preface to the second edition -- Contents -- 0. Introduction -- 1. Lévy processes and Itô calculus -- 2. Perturbations and properties of the probability law -- 3. Analysis of Wiener–Poisson functionals -- 4. Applications -- Appendix -- Bibliography -- List of symbols -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Calculus of variations. Jump processes. Malliavin calculus. Stochastic processes. Jump process. Lévy process. S.D.E. Stochastic calculus. MATHEMATICS / Probability & Statistics / General. bisacsh Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 9783110762501 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 9783110701005 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 9783110485103 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 9783110485288 ZDB-23-DMA EPUB 9783110392326 print 9783110377767 https://doi.org/10.1515/9783110378078 https://www.degruyter.com/isbn/9783110378078 Cover https://www.degruyter.com/document/cover/isbn/9783110378078/original |
language |
English |
format |
eBook |
author |
Ishikawa, Yasushi, Ishikawa, Yasushi, |
spellingShingle |
Ishikawa, Yasushi, Ishikawa, Yasushi, Stochastic Calculus of Variations : For Jump Processes / De Gruyter Studies in Mathematics , Frontmatter -- Preface -- Preface to the second edition -- Contents -- 0. Introduction -- 1. Lévy processes and Itô calculus -- 2. Perturbations and properties of the probability law -- 3. Analysis of Wiener–Poisson functionals -- 4. Applications -- Appendix -- Bibliography -- List of symbols -- Index |
author_facet |
Ishikawa, Yasushi, Ishikawa, Yasushi, |
author_variant |
y i yi y i yi |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Ishikawa, Yasushi, |
title |
Stochastic Calculus of Variations : For Jump Processes / |
title_sub |
For Jump Processes / |
title_full |
Stochastic Calculus of Variations : For Jump Processes / Yasushi Ishikawa. |
title_fullStr |
Stochastic Calculus of Variations : For Jump Processes / Yasushi Ishikawa. |
title_full_unstemmed |
Stochastic Calculus of Variations : For Jump Processes / Yasushi Ishikawa. |
title_auth |
Stochastic Calculus of Variations : For Jump Processes / |
title_alt |
Frontmatter -- Preface -- Preface to the second edition -- Contents -- 0. Introduction -- 1. Lévy processes and Itô calculus -- 2. Perturbations and properties of the probability law -- 3. Analysis of Wiener–Poisson functionals -- 4. Applications -- Appendix -- Bibliography -- List of symbols -- Index |
title_new |
Stochastic Calculus of Variations : |
title_sort |
stochastic calculus of variations : for jump processes / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2016 |
physical |
1 online resource (278 p.) Issued also in print. |
edition |
2nd ed. |
contents |
Frontmatter -- Preface -- Preface to the second edition -- Contents -- 0. Introduction -- 1. Lévy processes and Itô calculus -- 2. Perturbations and properties of the probability law -- 3. Analysis of Wiener–Poisson functionals -- 4. Applications -- Appendix -- Bibliography -- List of symbols -- Index |
isbn |
9783110378078 9783110762501 9783110701005 9783110494938 9783110485103 9783110485288 9783110392326 9783110377767 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110378078 https://www.degruyter.com/isbn/9783110378078 https://www.degruyter.com/document/cover/isbn/9783110378078/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
519 - Probabilities & applied mathematics |
dewey-full |
519.22 |
dewey-sort |
3519.2 12 |
dewey-raw |
519.2 2 |
dewey-search |
519.2 2 |
doi_str_mv |
10.1515/9783110378078 |
oclc_num |
949960367 |
work_keys_str_mv |
AT ishikawayasushi stochasticcalculusofvariationsforjumpprocesses |
status_str |
n |
ids_txt_mv |
(DE-B1597)429852 (OCoLC)949960367 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2016 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 |
is_hierarchy_title |
Stochastic Calculus of Variations : For Jump Processes / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 |
_version_ |
1770177585286742016 |
fullrecord |
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