Differential equations driven by rough paths: Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2007
|
| Schriftenreihe: | Lecture notes in mathematics
1908 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 109 S. graph. Darst. |
| ISBN: | 3540712844 9783540712848 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV022428391 | ||
| 003 | DE-604 | ||
| 005 | 20140120 | ||
| 007 | t | ||
| 008 | 070516s2007 d||| |||| 10||| eng d | ||
| 020 | |a 3540712844 |9 3-540-71284-4 | ||
| 020 | |a 9783540712848 |9 978-3-540-71284-8 | ||
| 035 | |a (OCoLC)255965299 | ||
| 035 | |a (DE-599)BVBBV022428391 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-91G |a DE-83 |a DE-11 |a DE-188 | ||
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a MAT 606f |2 stub | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a 60-06 |2 msc | ||
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Lyons, Terry J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential equations driven by rough paths |b Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |c Terry J. Lyons ; Michael Caruana ; Thierry Lévy |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XV, 109 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1908 | |
| 650 | 0 | 7 | |a Stochastisches Integral |0 (DE-588)4126478-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 2004 |z Saint-Flour |2 gnd-content | |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
| 689 | 0 | 1 | |a Stochastisches Integral |0 (DE-588)4126478-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Caruana, Michael |e Verfasser |4 aut | |
| 700 | 1 | |a Lévy, Thierry |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 1908 |w (DE-604)BV000676446 |9 1908 | |
| 856 | 4 | 2 | |m Digitalisierung TU Muenchen |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015636621 | ||
Datensatz im Suchindex
| _version_ | 1804136500296679424 |
|---|---|
| adam_text | Contents
Differential
Equations Driven by Moderately Irregular
Signals
.................................................... 1
1.1
Signals with Bounded Variation
........................... 1
1.1.1
The General Setting of Controlled Differential
Equations
........................................ 1
1.1.2
The Theorems of
Picard-Lindelöf
and Cauchy-Peano
................................ 2
1.2
Paths with Finite p-Variation
............................. 4
1.2.1
Definitions
....................................... 4
1.2.2
Controls
......................................... 6
1.2.3
Approximation Results
............................. 7
1.3
The Young Integral
...................................... 10
1.4
Differential Equations Driven by Signals with Finite
p-Variation, with
ρ
< 2................................... 13
1.4.1
Peano s Theorem
.................................. 13
1.4.2
Lipschitz Functions
................................ 15
1.4.3
Picard s Theorem
................................. 20
1.5
What Goes Wrong with
ρ
> 2............................. 21
1.5.1
No Continuous Extension of the
Stieltjes
Integral is
Rich Enough to Handle Brownian Paths
.............. 21
1.5.2
The Area Enclosed by a Path is Not a Continuous
Functional in Two-Variation
........................ 22
The Signature of a Path
................................... 25
2.1
Iterated Integrals and Linear Equations
.................... 25
2.2
The Signature of a Path
.................................. 28
2.2.1
Formal Series of Tensors
........................... 29
2.2.2
The Signature of a Path
............................ 30
2.2.3
Functions on the Range of the Signature
............. 33
2.2.4
Lie Elements, Logarithm and Exponential
............ 36
2.2.5
Truncated Signature and Free
Nilpotent
Groups
....... 37
2.2.6
The Signature of Paths with Bounded Variation
....... 39
XVIII
Contents
3
Rough Paths
.............................................. 41
3.1
Multiplicative
Funcţionale................................
41
3.1.1
Definition of Multiplicative Functional
.............. 41
3.1.2
Extension of Multiplicative Functional
.............. 45
3.1.3
Continuity of the Extension Map
.................... 51
3.2
Spaces of Rough Paths
................................... 52
3.2.1
Rough Paths and the p-Variation Topology
........... 52
3.2.2
Geometric Rough Paths
............................ 53
3.3
The Brownian Rough Path
............................... 55
3.3.1
The
Ito
Multiplicative Functional
.................... 55
3.3.2
The Stratonovich Multiplicative Functional
........... 56
3.3.3
New Noise Sources
................................ 58
4
Integration Along Rough Paths
............................ 63
4.1
Almost-Multiplicativity
.................................. 63
4.1.1
Almost-Additivity
................................. 63
4.1.2
Almost Rough Paths
............................... 65
4.2
Linear Differential Equations Driven by Rough Paths
........ 69
4.3
Integration of a One-form Along a Rough Path
.............. 73
4.3.1
Construction of an Almost Rough Path
.............. 73
4.3.2
Definition of the Integral
........................... 75
5
Differential Equations Driven by Rough Paths
............. 81
5.1
Linear Images of Geometric Rough Paths
................... 81
5.2
Solution of a Differential Equation Driven
by a Rough Path
........................................ 82
5.3
The Universal Limit Theorem
............................. 83
5.4
Linear Images and Comparison of Rough Paths
............. 84
5.5
Three
Picard
Iterations
.................................. 86
5.6
The Main Scaling Result
................................. 88
5.7
Uniform Control of the
Picard
Iterations
................... 89
5.8
Proof of the Main Theorem
............................... 91
References
..................................................... 95
Index
..........................................................101
List of Participants
............................................103
List of Short Lectures
.........................................107
|
| adam_txt |
Contents
Differential
Equations Driven by Moderately Irregular
Signals
. 1
1.1
Signals with Bounded Variation
. 1
1.1.1
The General Setting of Controlled Differential
Equations
. 1
1.1.2
The Theorems of
Picard-Lindelöf
and Cauchy-Peano
. 2
1.2
Paths with Finite p-Variation
. 4
1.2.1
Definitions
. 4
1.2.2
Controls
. 6
1.2.3
Approximation Results
. 7
1.3
The Young Integral
. 10
1.4
Differential Equations Driven by Signals with Finite
p-Variation, with
ρ
< 2. 13
1.4.1
Peano's Theorem
. 13
1.4.2
Lipschitz Functions
. 15
1.4.3
Picard's Theorem
. 20
1.5
What Goes Wrong with
ρ
> 2. 21
1.5.1
No Continuous Extension of the
Stieltjes
Integral is
Rich Enough to Handle Brownian Paths
. 21
1.5.2
The Area Enclosed by a Path is Not a Continuous
Functional in Two-Variation
. 22
The Signature of a Path
. 25
2.1
Iterated Integrals and Linear Equations
. 25
2.2
The Signature of a Path
. 28
2.2.1
Formal Series of Tensors
. 29
2.2.2
The Signature of a Path
. 30
2.2.3
Functions on the Range of the Signature
. 33
2.2.4
Lie Elements, Logarithm and Exponential
. 36
2.2.5
Truncated Signature and Free
Nilpotent
Groups
. 37
2.2.6
The Signature of Paths with Bounded Variation
. 39
XVIII
Contents
3
Rough Paths
. 41
3.1
Multiplicative
Funcţionale.
41
3.1.1
Definition of Multiplicative Functional
. 41
3.1.2
Extension of Multiplicative Functional
. 45
3.1.3
Continuity of the Extension Map
. 51
3.2
Spaces of Rough Paths
. 52
3.2.1
Rough Paths and the p-Variation Topology
. 52
3.2.2
Geometric Rough Paths
. 53
3.3
The Brownian Rough Path
. 55
3.3.1
The
Ito
Multiplicative Functional
. 55
3.3.2
The Stratonovich Multiplicative Functional
. 56
3.3.3
New Noise Sources
. 58
4
Integration Along Rough Paths
. 63
4.1
Almost-Multiplicativity
. 63
4.1.1
Almost-Additivity
. 63
4.1.2
Almost Rough Paths
. 65
4.2
Linear Differential Equations Driven by Rough Paths
. 69
4.3
Integration of a One-form Along a Rough Path
. 73
4.3.1
Construction of an Almost Rough Path
. 73
4.3.2
Definition of the Integral
. 75
5
Differential Equations Driven by Rough Paths
. 81
5.1
Linear Images of Geometric Rough Paths
. 81
5.2
Solution of a Differential Equation Driven
by a Rough Path
. 82
5.3
The Universal Limit Theorem
. 83
5.4
Linear Images and Comparison of Rough Paths
. 84
5.5
Three
Picard
Iterations
. 86
5.6
The Main Scaling Result
. 88
5.7
Uniform Control of the
Picard
Iterations
. 89
5.8
Proof of the Main Theorem
. 91
References
. 95
Index
.101
List of Participants
.103
List of Short Lectures
.107 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Lyons, Terry J. Caruana, Michael Lévy, Thierry |
| author_facet | Lyons, Terry J. Caruana, Michael Lévy, Thierry |
| author_role | aut aut aut |
| author_sort | Lyons, Terry J. |
| author_variant | t j l tj tjl m c mc t l tl |
| building | Verbundindex |
| bvnumber | BV022428391 |
| classification_rvk | SI 850 SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)255965299 (DE-599)BVBBV022428391 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01972nam a2200469 cb4500</leader><controlfield tag="001">BV022428391</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20140120 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">070516s2007 d||| |||| 10||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540712844</subfield><subfield code="9">3-540-71284-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540712848</subfield><subfield code="9">978-3-540-71284-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)255965299</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV022428391</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</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="084" ind1=" " ind2=" "><subfield code="a">MAT 606f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60-06</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lyons, Terry J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Differential equations driven by rough paths</subfield><subfield code="b">Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004</subfield><subfield code="c">Terry J. Lyons ; Michael Caruana ; Thierry Lévy</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 109 S.</subfield><subfield code="b">graph. Darst.</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1908</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">2004</subfield><subfield code="z">Saint-Flour</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische Differentialgleichung</subfield><subfield code="0">(DE-588)4057621-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</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">Caruana, Michael</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lévy, Thierry</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1908</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1908</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung TU Muenchen</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015636621</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift 2004 Saint-Flour gnd-content |
| genre_facet | Konferenzschrift 2004 Saint-Flour |
| id | DE-604.BV022428391 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:28:19Z |
| indexdate | 2024-07-09T20:57:23Z |
| institution | BVB |
| isbn | 3540712844 9783540712848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015636621 |
| oclc_num | 255965299 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XV, 109 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Lyons, Terry J. Verfasser aut Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 Terry J. Lyons ; Michael Caruana ; Thierry Lévy Berlin [u.a.] Springer 2007 XV, 109 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1908 Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2004 Saint-Flour gnd-content Stochastische Differentialgleichung (DE-588)4057621-8 s Stochastisches Integral (DE-588)4126478-2 s DE-604 Caruana, Michael Verfasser aut Lévy, Thierry Verfasser aut Lecture notes in mathematics 1908 (DE-604)BV000676446 1908 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lyons, Terry J. Caruana, Michael Lévy, Thierry Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 Lecture notes in mathematics Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4057621-8 (DE-588)1071861417 |
| title | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |
| title_auth | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |
| title_exact_search | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |
| title_exact_search_txtP | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |
| title_full | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 Terry J. Lyons ; Michael Caruana ; Thierry Lévy |
| title_fullStr | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 Terry J. Lyons ; Michael Caruana ; Thierry Lévy |
| title_full_unstemmed | Differential equations driven by rough paths Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 Terry J. Lyons ; Michael Caruana ; Thierry Lévy |
| title_short | Differential equations driven by rough paths |
| title_sort | differential equations driven by rough paths ecole d ete de probabilites de saint flour xxxiv 2004 |
| title_sub | Ècole d'Été de Probabilités de Saint-Flour XXXIV - 2004 |
| topic | Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastisches Integral Stochastische Differentialgleichung Konferenzschrift 2004 Saint-Flour |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015636621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT lyonsterryj differentialequationsdrivenbyroughpathsecoledetedeprobabilitesdesaintflourxxxiv2004 AT caruanamichael differentialequationsdrivenbyroughpathsecoledetedeprobabilitesdesaintflourxxxiv2004 AT levythierry differentialequationsdrivenbyroughpathsecoledetedeprobabilitesdesaintflourxxxiv2004 |