Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2010
|
| Series: | Memoirs of the American Mathematical Society
960 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 204, number 960 (fourth of 5 numbers ) Literaturverz.: S.73 - 77 |
| Physical Description: | V, 77 S. |
| ISBN: | 9780821847152 |
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MARC
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| 245 | 1 | 0 | |a Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations |c Olivier Alvarez, Martino Bardi |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 2010 | |
| 300 | |a V, 77 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 960 | |
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| 650 | 4 | |a Singular perturbations (Mathematics) | |
| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
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| adam_text | Contents
Chapter
1.
Introduction and statement of the problem
1
1.1.
Introduction
ι
1.2.
Stochastic differential games and the singular perturbation problem
6
1.3.
The Bellman-Isaacs equations
8
Chapter
2.
Abstract ergodicity, stabilization, and convergence
11
2.1.
Ergodicity and the effective Hamiltonian
Ц
2.2.
Stabilization and the effective terminal cost
15
2.3.
The general convergence result
17
Chapter
3.
Uncontrolled fast variables and averaging
21
3.1.
Ergodicity
22
3.2.
Stabilization
23
3.3.
Uniform convergence
24
3.4.
An explicit formula for the limit control problem
26
Chapter
4.
Uniformly
nondegenerate
fast diffusion
29
4.1.
Ergodicity
29
4.2.
Stabilization
31
4.3.
Uniform convergence
33
Chapter
5.
Hypoelliptic diffusion of the fast variables
37
5.1.
Ergodicity and stabilization
38
5.2.
Uniform convergence
39
Chapter
6.
Controllable fast variables
41
6.1.
Bounded-time controllability and ergodicity
41
6.2.
Stabilization and a formula for the effective initial data
46
6.3.
An explicit formula for the effective Hamiltonian and the limit
differential game
47
6.4.
Uniform convergence
50
6.5.
The reduction order formula for the effective control problem
52
Chapter
7.
Nonresonant
fast variables
55
7.1.
Ergodicity
55
7.2.
Stabilization
57
7.3.
Uniform convergence
60
Chapter
8.
A counterexample to uniform convergence
61
Chapter
9.
Applications to homogenization
67
9.1.
Periodic homogenization of
1st
order
Н
-J
equations
67
CONTENTS
9.2.
Periodic bomogenization
of
2nd
order equations
69
Bibliography
73
|
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV036084728 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:12Z |
| institution | BVB |
| isbn | 9780821847152 |
| language | English |
| lccn | 2009049941 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018975711 |
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| physical | V, 77 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Alvarez, Olivier 1969- Verfasser (DE-588)140795251 aut Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations Olivier Alvarez, Martino Bardi Providence, R.I. American Math. Soc. 2010 V, 77 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 960 Volume 204, number 960 (fourth of 5 numbers ) Literaturverz.: S.73 - 77 Singular perturbations (Mathematics) Differential equations, Partial Differential games Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Bardi, Martino 1956- Verfasser (DE-588)115277463 aut Memoirs of the American Mathematical Society 960 (DE-604)BV008000141 960 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018975711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alvarez, Olivier 1969- Bardi, Martino 1956- Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations Memoirs of the American Mathematical Society Singular perturbations (Mathematics) Differential equations, Partial Differential games Partielle Differentialgleichung (DE-588)4044779-0 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4055100-3 |
| title | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations |
| title_auth | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations |
| title_exact_search | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations |
| title_full | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations Olivier Alvarez, Martino Bardi |
| title_fullStr | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations Olivier Alvarez, Martino Bardi |
| title_full_unstemmed | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations Olivier Alvarez, Martino Bardi |
| title_short | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations |
| title_sort | ergodicity stabilization and singular perturbations for bellman isaacs equations |
| topic | Singular perturbations (Mathematics) Differential equations, Partial Differential games Partielle Differentialgleichung (DE-588)4044779-0 gnd Singuläre Störung (DE-588)4055100-3 gnd |
| topic_facet | Singular perturbations (Mathematics) Differential equations, Partial Differential games Partielle Differentialgleichung Singuläre Störung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018975711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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