Probability Theory III: Stochastic Calculus
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
45 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t |
| Beschreibung: | 1 Online-Ressource (VI, 256 p) |
| ISBN: | 9783662036402 9783642081224 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-03640-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423273 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1998 |||| o||u| ||||||eng d | ||
| 020 | |a 9783662036402 |c Online |9 978-3-662-03640-2 | ||
| 020 | |a 9783642081224 |c Print |9 978-3-642-08122-4 | ||
| 024 | 7 | |a 10.1007/978-3-662-03640-2 |2 doi | |
| 035 | |a (OCoLC)863882043 | ||
| 035 | |a (DE-599)BVBBV042423273 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 519.2 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Prokhorov, Yu. V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probability Theory III |b Stochastic Calculus |c by Yu. V. Prokhorov, A. N. Shiryaev |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1998 | |
| 300 | |a 1 Online-Ressource (VI, 256 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopaedia of Mathematical Sciences |v 45 |x 0938-0396 | |
| 500 | |a Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Statistics | |
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Statistics, general | |
| 650 | 4 | |a Computational Intelligence | |
| 650 | 4 | |a Finance/Investment/Banking | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Statistik | |
| 700 | 1 | |a Shiryaev, A. N. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-03640-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858690 | ||
Datensatz im Suchindex
| _version_ | 1804153098815406080 |
|---|---|
| any_adam_object | |
| author | Prokhorov, Yu. V. |
| author_facet | Prokhorov, Yu. V. |
| author_role | aut |
| author_sort | Prokhorov, Yu. V. |
| author_variant | y v p yv yvp |
| building | Verbundindex |
| bvnumber | BV042423273 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863882043 (DE-599)BVBBV042423273 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03640-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02970nmm a2200505zcb4500</leader><controlfield tag="001">BV042423273</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1998 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662036402</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-03640-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642081224</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-08122-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-03640-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863882043</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423273</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Prokhorov, Yu. V.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Probability Theory III</subfield><subfield code="b">Stochastic Calculus</subfield><subfield code="c">by Yu. V. Prokhorov, A. N. Shiryaev</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VI, 256 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Encyclopaedia of Mathematical Sciences</subfield><subfield code="v">45</subfield><subfield code="x">0938-0396</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational Intelligence</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finance/Investment/Banking</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ingenieurwissenschaften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistik</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Shiryaev, A. N.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-03640-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858690</subfield></datafield></record></collection> |
| id | DE-604.BV042423273 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662036402 9783642081224 |
| issn | 0938-0396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858690 |
| oclc_num | 863882043 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VI, 256 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Prokhorov, Yu. V. Verfasser aut Probability Theory III Stochastic Calculus by Yu. V. Prokhorov, A. N. Shiryaev Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource (VI, 256 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 45 0938-0396 Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t Mathematics Distribution (Probability theory) Statistics Engineering Probability Theory and Stochastic Processes Statistics, general Computational Intelligence Finance/Investment/Banking Ingenieurwissenschaften Mathematik Statistik Shiryaev, A. N. Sonstige oth https://doi.org/10.1007/978-3-662-03640-2 Verlag Volltext |
| spellingShingle | Prokhorov, Yu. V. Probability Theory III Stochastic Calculus Mathematics Distribution (Probability theory) Statistics Engineering Probability Theory and Stochastic Processes Statistics, general Computational Intelligence Finance/Investment/Banking Ingenieurwissenschaften Mathematik Statistik |
| title | Probability Theory III Stochastic Calculus |
| title_auth | Probability Theory III Stochastic Calculus |
| title_exact_search | Probability Theory III Stochastic Calculus |
| title_full | Probability Theory III Stochastic Calculus by Yu. V. Prokhorov, A. N. Shiryaev |
| title_fullStr | Probability Theory III Stochastic Calculus by Yu. V. Prokhorov, A. N. Shiryaev |
| title_full_unstemmed | Probability Theory III Stochastic Calculus by Yu. V. Prokhorov, A. N. Shiryaev |
| title_short | Probability Theory III |
| title_sort | probability theory iii stochastic calculus |
| title_sub | Stochastic Calculus |
| topic | Mathematics Distribution (Probability theory) Statistics Engineering Probability Theory and Stochastic Processes Statistics, general Computational Intelligence Finance/Investment/Banking Ingenieurwissenschaften Mathematik Statistik |
| topic_facet | Mathematics Distribution (Probability theory) Statistics Engineering Probability Theory and Stochastic Processes Statistics, general Computational Intelligence Finance/Investment/Banking Ingenieurwissenschaften Mathematik Statistik |
| url | https://doi.org/10.1007/978-3-662-03640-2 |
| work_keys_str_mv | AT prokhorovyuv probabilitytheoryiiistochasticcalculus AT shiryaevan probabilitytheoryiiistochasticcalculus |