Brownian Motion : : A Guide to Random Processes and Stochastic Calculus / / René L. Schilling.
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special...
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2021] ©2021 |
| Year of Publication: | 2021 |
| Edition: | 3rd Edition |
| Language: | English |
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| Physical Description: | 1 online resource (XIV, 519 p.) |
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Schilling, René L., author. aut http://id.loc.gov/vocabulary/relators/aut Brownian Motion : A Guide to Random Processes and Stochastic Calculus / René L. Schilling. 3rd Edition Berlin ; Boston : De Gruyter, [2021] ©2021 1 online resource (XIV, 519 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Preface -- Contents -- Dependence chart -- 1 Robert Brown’s new thing -- 2 Brownian motion as a Gaussian process -- 3 Constructions of Brownian motion -- 4 The canonical model -- 5 Brownian motion as a martingale -- 6 Brownian motion as a Markov process -- 7 Brownian motion and transition semigroups -- 8 The PDE connection -- 9 The variation of Brownian paths -- 10 Regularity of Brownian paths -- 11 Brownian motion as a random fractal -- 12 The growth of Brownian paths -- 13 Strassen’s functional law of the iterated logarithm -- 14 Skorokhod representation -- 15 Stochastic integrals: L2-Theory -- 16 Stochastic integrals: localization -- 17 Stochastic integrals: martingale drivers -- 18 Itô’s formula -- 19 Applications of Itô’s formula -- 20 Wiener Chaos and iterated Wiener–Itô integrals -- 21 Stochastic differential equations -- 22 Stratonovich’s stochastic calculus -- 23 On diffusions -- 24 Simulation of Brownian motion by Björn Böttcher -- A Appendix -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''. 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 01. Dez 2022) Brownian motion processes. Stochastic processes. Brownsche Bewegung. Finanzmathematik. Pfadeigenschaften. Stochastische Prozesse. MATHEMATICS / Probability & Statistics / General. bisacsh Böttcher, Björn, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter DG Ebook Package English 2021 9783110750720 Title is part of eBook package: De Gruyter DG Plus DeG Package 2021 Part 1 9783110750706 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English 9783110754001 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 9783110753776 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 English 9783110754131 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 9783110753905 ZDB-23-DMA EPUB 9783110741490 print 9783110741254 https://doi.org/10.1515/9783110741278 https://www.degruyter.com/isbn/9783110741278 Cover https://www.degruyter.com/document/cover/isbn/9783110741278/original |
| language |
English |
| format |
eBook |
| author |
Schilling, René L., Schilling, René L., |
| spellingShingle |
Schilling, René L., Schilling, René L., Brownian Motion : A Guide to Random Processes and Stochastic Calculus / De Gruyter Textbook Frontmatter -- Preface -- Contents -- Dependence chart -- 1 Robert Brown’s new thing -- 2 Brownian motion as a Gaussian process -- 3 Constructions of Brownian motion -- 4 The canonical model -- 5 Brownian motion as a martingale -- 6 Brownian motion as a Markov process -- 7 Brownian motion and transition semigroups -- 8 The PDE connection -- 9 The variation of Brownian paths -- 10 Regularity of Brownian paths -- 11 Brownian motion as a random fractal -- 12 The growth of Brownian paths -- 13 Strassen’s functional law of the iterated logarithm -- 14 Skorokhod representation -- 15 Stochastic integrals: L2-Theory -- 16 Stochastic integrals: localization -- 17 Stochastic integrals: martingale drivers -- 18 Itô’s formula -- 19 Applications of Itô’s formula -- 20 Wiener Chaos and iterated Wiener–Itô integrals -- 21 Stochastic differential equations -- 22 Stratonovich’s stochastic calculus -- 23 On diffusions -- 24 Simulation of Brownian motion by Björn Böttcher -- A Appendix -- Bibliography -- Index |
| author_facet |
Schilling, René L., Schilling, René L., Böttcher, Björn, Böttcher, Björn, |
| author_variant |
r l s rl rls r l s rl rls |
| author_role |
VerfasserIn VerfasserIn |
| author2 |
Böttcher, Björn, Böttcher, Björn, |
| author2_variant |
b b bb b b bb |
| author2_role |
MitwirkendeR MitwirkendeR |
| author_sort |
Schilling, René L., |
| title |
Brownian Motion : A Guide to Random Processes and Stochastic Calculus / |
| title_sub |
A Guide to Random Processes and Stochastic Calculus / |
| title_full |
Brownian Motion : A Guide to Random Processes and Stochastic Calculus / René L. Schilling. |
| title_fullStr |
Brownian Motion : A Guide to Random Processes and Stochastic Calculus / René L. Schilling. |
| title_full_unstemmed |
Brownian Motion : A Guide to Random Processes and Stochastic Calculus / René L. Schilling. |
| title_auth |
Brownian Motion : A Guide to Random Processes and Stochastic Calculus / |
| title_alt |
Frontmatter -- Preface -- Contents -- Dependence chart -- 1 Robert Brown’s new thing -- 2 Brownian motion as a Gaussian process -- 3 Constructions of Brownian motion -- 4 The canonical model -- 5 Brownian motion as a martingale -- 6 Brownian motion as a Markov process -- 7 Brownian motion and transition semigroups -- 8 The PDE connection -- 9 The variation of Brownian paths -- 10 Regularity of Brownian paths -- 11 Brownian motion as a random fractal -- 12 The growth of Brownian paths -- 13 Strassen’s functional law of the iterated logarithm -- 14 Skorokhod representation -- 15 Stochastic integrals: L2-Theory -- 16 Stochastic integrals: localization -- 17 Stochastic integrals: martingale drivers -- 18 Itô’s formula -- 19 Applications of Itô’s formula -- 20 Wiener Chaos and iterated Wiener–Itô integrals -- 21 Stochastic differential equations -- 22 Stratonovich’s stochastic calculus -- 23 On diffusions -- 24 Simulation of Brownian motion by Björn Böttcher -- A Appendix -- Bibliography -- Index |
| title_new |
Brownian Motion : |
| title_sort |
brownian motion : a guide to random processes and stochastic calculus / |
| series |
De Gruyter Textbook |
| series2 |
De Gruyter Textbook |
| publisher |
De Gruyter, |
| publishDate |
2021 |
| physical |
1 online resource (XIV, 519 p.) Issued also in print. |
| edition |
3rd Edition |
| contents |
Frontmatter -- Preface -- Contents -- Dependence chart -- 1 Robert Brown’s new thing -- 2 Brownian motion as a Gaussian process -- 3 Constructions of Brownian motion -- 4 The canonical model -- 5 Brownian motion as a martingale -- 6 Brownian motion as a Markov process -- 7 Brownian motion and transition semigroups -- 8 The PDE connection -- 9 The variation of Brownian paths -- 10 Regularity of Brownian paths -- 11 Brownian motion as a random fractal -- 12 The growth of Brownian paths -- 13 Strassen’s functional law of the iterated logarithm -- 14 Skorokhod representation -- 15 Stochastic integrals: L2-Theory -- 16 Stochastic integrals: localization -- 17 Stochastic integrals: martingale drivers -- 18 Itô’s formula -- 19 Applications of Itô’s formula -- 20 Wiener Chaos and iterated Wiener–Itô integrals -- 21 Stochastic differential equations -- 22 Stratonovich’s stochastic calculus -- 23 On diffusions -- 24 Simulation of Brownian motion by Björn Böttcher -- A Appendix -- Bibliography -- Index |
| isbn |
9783110741278 9783110750720 9783110750706 9783110754001 9783110753776 9783110754131 9783110753905 9783110741490 9783110741254 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA274 |
| callnumber-sort |
QA 3274.75 S35 42021 |
| url |
https://doi.org/10.1515/9783110741278 https://www.degruyter.com/isbn/9783110741278 https://www.degruyter.com/document/cover/isbn/9783110741278/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
519 - Probabilities & applied mathematics |
| dewey-full |
519.2/33 |
| dewey-sort |
3519.2 233 |
| dewey-raw |
519.2/33 |
| dewey-search |
519.2/33 |
| doi_str_mv |
10.1515/9783110741278 |
| oclc_num |
1266228052 |
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AT schillingrenel brownianmotionaguidetorandomprocessesandstochasticcalculus AT bottcherbjorn brownianmotionaguidetorandomprocessesandstochasticcalculus |
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Brownian Motion : A Guide to Random Processes and Stochastic Calculus / |
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