Non-homogeneous random walks: Lyapunov function methods for near-critical stochastic systems
Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain cr...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2017
|
| Series: | Cambridge tracts in mathematics
209 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems |
| Physical Description: | 1 Online-Ressource (xviii, 363 Seiten) |
| ISBN: | 9781139208468 |
| DOI: | 10.1017/9781139208468 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV044243355 | ||
| 003 | DE-604 | ||
| 005 | 20190423 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 170327s2017 |||| o||u| ||||||eng d | ||
| 020 | |a 9781139208468 |9 978-1-139-20846-8 | ||
| 024 | 7 | |a 10.1017/9781139208468 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781139208468 | ||
| 035 | |a (OCoLC)992524308 | ||
| 035 | |a (DE-599)BVBBV044243355 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-355 | ||
| 082 | 0 | |a 519.2/82 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 100 | 1 | |a Menšikov, Michail Vasilʹevič |e Verfasser |0 (DE-588)1067821546 |4 aut | |
| 245 | 1 | 0 | |a Non-homogeneous random walks |b Lyapunov function methods for near-critical stochastic systems |c Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2017 | |
| 300 | |a 1 Online-Ressource (xviii, 363 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge tracts in mathematics |v 209 | |
| 520 | |a Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems | ||
| 650 | 4 | |a Random walks (Mathematics) | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Irrfahrtsproblem |0 (DE-588)4162442-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Irrfahrtsproblem |0 (DE-588)4162442-7 |D s |
| 689 | 0 | 1 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Popov, Serguéi |d 1972- |e Verfasser |0 (DE-588)1137240407 |4 aut | |
| 700 | 1 | |a Wade, Andrew |d 1981- |e Verfasser |0 (DE-588)1122867123 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, hardback |z 978-1-107-02669-8 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781139208468 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029648636 | ||
| 966 | e | |u https://doi.org/10.1017/9781139208468 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781139208468 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781139208468 |l UBR01 |p ZDB-20-CBO |q UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804177406200643584 |
|---|---|
| any_adam_object | |
| author | Menšikov, Michail Vasilʹevič Popov, Serguéi 1972- Wade, Andrew 1981- |
| author_GND | (DE-588)1067821546 (DE-588)1137240407 (DE-588)1122867123 |
| author_facet | Menšikov, Michail Vasilʹevič Popov, Serguéi 1972- Wade, Andrew 1981- |
| author_role | aut aut aut |
| author_sort | Menšikov, Michail Vasilʹevič |
| author_variant | m v m mv mvm s p sp a w aw |
| building | Verbundindex |
| bvnumber | BV044243355 |
| classification_rvk | SK 820 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781139208468 (OCoLC)992524308 (DE-599)BVBBV044243355 |
| dewey-full | 519.2/82 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/82 |
| dewey-search | 519.2/82 |
| dewey-sort | 3519.2 282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781139208468 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03295nmm a2200505zcb4500</leader><controlfield tag="001">BV044243355</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190423 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">170327s2017 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139208468</subfield><subfield code="9">978-1-139-20846-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781139208468</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781139208468</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992524308</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044243355</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/82</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Menšikov, Michail Vasilʹevič</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1067821546</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Non-homogeneous random walks</subfield><subfield code="b">Lyapunov function methods for near-critical stochastic systems</subfield><subfield code="c">Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xviii, 363 Seiten)</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">Cambridge tracts in mathematics</subfield><subfield code="v">209</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random walks (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Irrfahrtsproblem</subfield><subfield code="0">(DE-588)4162442-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Irrfahrtsproblem</subfield><subfield code="0">(DE-588)4162442-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Popov, Serguéi</subfield><subfield code="d">1972-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1137240407</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wade, Andrew</subfield><subfield code="d">1981-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1122867123</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, hardback</subfield><subfield code="z">978-1-107-02669-8</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781139208468</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029648636</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781139208468</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781139208468</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781139208468</subfield><subfield code="l">UBR01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBR Einzelkauf (Lückenergänzung CUP Serien 2018)</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044243355 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:47:34Z |
| institution | BVB |
| isbn | 9781139208468 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029648636 |
| oclc_num | 992524308 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xviii, 363 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Menšikov, Michail Vasilʹevič Verfasser (DE-588)1067821546 aut Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham Cambridge Cambridge University Press 2017 1 Online-Ressource (xviii, 363 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 209 Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems Random walks (Mathematics) Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Popov, Serguéi 1972- Verfasser (DE-588)1137240407 aut Wade, Andrew 1981- Verfasser (DE-588)1122867123 aut Erscheint auch als Druck-Ausgabe, hardback 978-1-107-02669-8 https://doi.org/10.1017/9781139208468 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Menšikov, Michail Vasilʹevič Popov, Serguéi 1972- Wade, Andrew 1981- Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems Random walks (Mathematics) Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4162442-7 |
| title | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems |
| title_auth | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems |
| title_exact_search | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems |
| title_full | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham |
| title_fullStr | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham |
| title_full_unstemmed | Non-homogeneous random walks Lyapunov function methods for near-critical stochastic systems Mikhail Menshikov, University of Durham, Serguei Popov, Universidade Estadual de Campinas, Brazil, Andrew Wade, University of Durham |
| title_short | Non-homogeneous random walks |
| title_sort | non homogeneous random walks lyapunov function methods for near critical stochastic systems |
| title_sub | Lyapunov function methods for near-critical stochastic systems |
| topic | Random walks (Mathematics) Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd |
| topic_facet | Random walks (Mathematics) Stochastic processes Stochastischer Prozess Irrfahrtsproblem |
| url | https://doi.org/10.1017/9781139208468 |
| work_keys_str_mv | AT mensikovmichailvasilʹevic nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems AT popovserguei nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems AT wadeandrew nonhomogeneousrandomwalkslyapunovfunctionmethodsfornearcriticalstochasticsystems |