Brownian motion :: an introduction to stochastic processes /
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has infl...
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
©2012.
|
| Schriftenreihe: | De Gruyter graduate.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors' aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion. |
| Beschreibung: | 1 online resource (xiv, 380 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110278989 3110278987 3110278898 9783110278897 |
Internformat
MARC
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| 100 | 1 | |a Schilling, René L. | |
| 245 | 1 | 0 | |a Brownian motion : |b an introduction to stochastic processes / |c René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher. |
| 260 | |a Berlin ; |a Boston : |b De Gruyter, |c ©2012. | ||
| 300 | |a 1 online resource (xiv, 380 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Robert Brown's new thing -- Brownian motion as a Gaussian process -- Constructions of Brownian motion -- The canonical model -- Brownian motion as a martingale -- Brownian motion as a Markov process -- Brownian motion and transition semigroups -- The PDE connection -- The variation of Brownian paths -- Regularity of Brownian paths -- Strassen's functional law of the iterated logarithm -- Skorokhod representation -- Stochastic integrals: L²-theory -- Stochastic integrals: beyond -- Itô's formula -- Application of Itô's formula -- Stochastic differential equations -- On diffusions -- Simulation of Brownian motion / Björn Böttcher -- Appendixes: A.1. Kolmogorov's existence theorem -- A.2. A property of conditional expectations -- A.3. From discrete to continuous time martigales -- A.4. Stopping and sampling -- A.5. Remarks on Feller processes -- A.6. The Doob-Meyer decomposition -- A.7. BV functions and Riemann-Stieltjes integrals -- A.8. Some tools from analysis. | |
| 520 | |a Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors' aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion. | ||
| 650 | 0 | |a Brownian motion processes. |0 http://id.loc.gov/authorities/subjects/sh85017265 | |
| 650 | 0 | |a Stochastic processes. |0 http://id.loc.gov/authorities/subjects/sh85128181 | |
| 650 | 6 | |a Processus de mouvement brownien. | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Brownian motion processes |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 650 | 7 | |a Brownsche Bewegung |2 gnd |0 http://d-nb.info/gnd/4128328-4 | |
| 650 | 7 | |a Stochastischer Prozess |2 gnd |0 http://d-nb.info/gnd/4057630-9 | |
| 700 | 1 | |a Partzsch, Lothar, |d 1945- |1 https://id.oclc.org/worldcat/entity/E39PCjrmW38FKwb4h4qV4tkGVC |0 http://id.loc.gov/authorities/names/n85059245 | |
| 700 | 1 | |a Böttcher, Björn. | |
| 776 | 0 | 8 | |i Print version: |a Schilling, René L. |t Brownian motion. |d Berlin ; Boston : De Gruyter, ©2012 |w (DLC) 2012007045 |
| 830 | 0 | |a De Gruyter graduate. |0 http://id.loc.gov/authorities/names/no2011117424 | |
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Datensatz im Suchindex
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| _version_ | 1816882204653912065 |
| adam_text | |
| any_adam_object | |
| author | Schilling, René L. |
| author2 | Partzsch, Lothar, 1945- Böttcher, Björn |
| author2_role | |
| author2_variant | l p lp b b bb |
| author_GND | http://id.loc.gov/authorities/names/n85059245 |
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| contents | Robert Brown's new thing -- Brownian motion as a Gaussian process -- Constructions of Brownian motion -- The canonical model -- Brownian motion as a martingale -- Brownian motion as a Markov process -- Brownian motion and transition semigroups -- The PDE connection -- The variation of Brownian paths -- Regularity of Brownian paths -- Strassen's functional law of the iterated logarithm -- Skorokhod representation -- Stochastic integrals: L²-theory -- Stochastic integrals: beyond -- Itô's formula -- Application of Itô's formula -- Stochastic differential equations -- On diffusions -- Simulation of Brownian motion / Björn Böttcher -- Appendixes: A.1. Kolmogorov's existence theorem -- A.2. A property of conditional expectations -- A.3. From discrete to continuous time martigales -- A.4. Stopping and sampling -- A.5. Remarks on Feller processes -- A.6. The Doob-Meyer decomposition -- A.7. BV functions and Riemann-Stieltjes integrals -- A.8. Some tools from analysis. |
| ctrlnum | (OCoLC)808342286 |
| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn808342286 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:24:54Z |
| institution | BVB |
| isbn | 9783110278989 3110278987 3110278898 9783110278897 |
| language | English |
| oclc_num | 808342286 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 380 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter graduate. |
| series2 | De Gruyter graduate |
| spelling | Schilling, René L. Brownian motion : an introduction to stochastic processes / René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher. Berlin ; Boston : De Gruyter, ©2012. 1 online resource (xiv, 380 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter graduate Includes bibliographical references and index. Robert Brown's new thing -- Brownian motion as a Gaussian process -- Constructions of Brownian motion -- The canonical model -- Brownian motion as a martingale -- Brownian motion as a Markov process -- Brownian motion and transition semigroups -- The PDE connection -- The variation of Brownian paths -- Regularity of Brownian paths -- Strassen's functional law of the iterated logarithm -- Skorokhod representation -- Stochastic integrals: L²-theory -- Stochastic integrals: beyond -- Itô's formula -- Application of Itô's formula -- Stochastic differential equations -- On diffusions -- Simulation of Brownian motion / Björn Böttcher -- Appendixes: A.1. Kolmogorov's existence theorem -- A.2. A property of conditional expectations -- A.3. From discrete to continuous time martigales -- A.4. Stopping and sampling -- A.5. Remarks on Feller processes -- A.6. The Doob-Meyer decomposition -- A.7. BV functions and Riemann-Stieltjes integrals -- A.8. Some tools from analysis. Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors' aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion. Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Stochastischer Prozess gnd http://d-nb.info/gnd/4057630-9 Partzsch, Lothar, 1945- https://id.oclc.org/worldcat/entity/E39PCjrmW38FKwb4h4qV4tkGVC http://id.loc.gov/authorities/names/n85059245 Böttcher, Björn. Print version: Schilling, René L. Brownian motion. Berlin ; Boston : De Gruyter, ©2012 (DLC) 2012007045 De Gruyter graduate. http://id.loc.gov/authorities/names/no2011117424 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=471068 Volltext |
| spellingShingle | Schilling, René L. Brownian motion : an introduction to stochastic processes / De Gruyter graduate. Robert Brown's new thing -- Brownian motion as a Gaussian process -- Constructions of Brownian motion -- The canonical model -- Brownian motion as a martingale -- Brownian motion as a Markov process -- Brownian motion and transition semigroups -- The PDE connection -- The variation of Brownian paths -- Regularity of Brownian paths -- Strassen's functional law of the iterated logarithm -- Skorokhod representation -- Stochastic integrals: L²-theory -- Stochastic integrals: beyond -- Itô's formula -- Application of Itô's formula -- Stochastic differential equations -- On diffusions -- Simulation of Brownian motion / Björn Böttcher -- Appendixes: A.1. Kolmogorov's existence theorem -- A.2. A property of conditional expectations -- A.3. From discrete to continuous time martigales -- A.4. Stopping and sampling -- A.5. Remarks on Feller processes -- A.6. The Doob-Meyer decomposition -- A.7. BV functions and Riemann-Stieltjes integrals -- A.8. Some tools from analysis. Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Stochastischer Prozess gnd http://d-nb.info/gnd/4057630-9 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85017265 http://id.loc.gov/authorities/subjects/sh85128181 http://d-nb.info/gnd/4128328-4 http://d-nb.info/gnd/4057630-9 |
| title | Brownian motion : an introduction to stochastic processes / |
| title_auth | Brownian motion : an introduction to stochastic processes / |
| title_exact_search | Brownian motion : an introduction to stochastic processes / |
| title_full | Brownian motion : an introduction to stochastic processes / René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher. |
| title_fullStr | Brownian motion : an introduction to stochastic processes / René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher. |
| title_full_unstemmed | Brownian motion : an introduction to stochastic processes / René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher. |
| title_short | Brownian motion : |
| title_sort | brownian motion an introduction to stochastic processes |
| title_sub | an introduction to stochastic processes / |
| topic | Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Stochastischer Prozess gnd http://d-nb.info/gnd/4057630-9 |
| topic_facet | Brownian motion processes. Stochastic processes. Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. Brownian motion processes Stochastic processes Brownsche Bewegung Stochastischer Prozess |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=471068 |
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