Stochastic Controls: Hamiltonian Systems and HJB Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Applications of Mathematics, Stochastic Modelling and Applied Probability
43 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the following: (Q) What is the relationship betwccn the maximum principlc and dynamic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equation, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second order in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation |
| Beschreibung: | 1 Online-Ressource (XXII, 439 p) |
| ISBN: | 9781461214663 9781461271543 |
| ISSN: | 0172-4568 |
| DOI: | 10.1007/978-1-4612-1466-3 |
Internformat
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| 100 | 1 | |a Yong, Jiongmin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic Controls |b Hamiltonian Systems and HJB Equations |c by Jiongmin Yong, Xun Yu Zhou |
| 264 | 1 | |a New York, NY |b Springer New York |c 1999 | |
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| 490 | 1 | |a Applications of Mathematics, Stochastic Modelling and Applied Probability |v 43 |x 0172-4568 | |
| 500 | |a As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the following: (Q) What is the relationship betwccn the maximum principlc and dynamic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equation, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second order in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation | ||
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Datensatz im Suchindex
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| author | Yong, Jiongmin |
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| 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 | 10.1007/978-1-4612-1466-3 |
| format | Electronic eBook |
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| id | DE-604.BV042419836 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461214663 9781461271543 |
| issn | 0172-4568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855253 |
| oclc_num | 863675963 |
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| physical | 1 Online-Ressource (XXII, 439 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| series | Applications of Mathematics, Stochastic Modelling and Applied Probability |
| series2 | Applications of Mathematics, Stochastic Modelling and Applied Probability |
| spelling | Yong, Jiongmin Verfasser aut Stochastic Controls Hamiltonian Systems and HJB Equations by Jiongmin Yong, Xun Yu Zhou New York, NY Springer New York 1999 1 Online-Ressource (XXII, 439 p) txt rdacontent c rdamedia cr rdacarrier Applications of Mathematics, Stochastic Modelling and Applied Probability 43 0172-4568 As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the following: (Q) What is the relationship betwccn the maximum principlc and dynamic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equation, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second order in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s 1\p DE-604 Zhou, Xun Yu Sonstige oth Applications of Mathematics, Stochastic Modelling and Applied Probability 43 (DE-604)BV000895226 43 https://doi.org/10.1007/978-1-4612-1466-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yong, Jiongmin Stochastic Controls Hamiltonian Systems and HJB Equations Applications of Mathematics, Stochastic Modelling and Applied Probability Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| subject_GND | (DE-588)4263657-7 |
| title | Stochastic Controls Hamiltonian Systems and HJB Equations |
| title_auth | Stochastic Controls Hamiltonian Systems and HJB Equations |
| title_exact_search | Stochastic Controls Hamiltonian Systems and HJB Equations |
| title_full | Stochastic Controls Hamiltonian Systems and HJB Equations by Jiongmin Yong, Xun Yu Zhou |
| title_fullStr | Stochastic Controls Hamiltonian Systems and HJB Equations by Jiongmin Yong, Xun Yu Zhou |
| title_full_unstemmed | Stochastic Controls Hamiltonian Systems and HJB Equations by Jiongmin Yong, Xun Yu Zhou |
| title_short | Stochastic Controls |
| title_sort | stochastic controls hamiltonian systems and hjb equations |
| title_sub | Hamiltonian Systems and HJB Equations |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Stochastische Kontrolltheorie |
| url | https://doi.org/10.1007/978-1-4612-1466-3 |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT yongjiongmin stochasticcontrolshamiltoniansystemsandhjbequations AT zhouxunyu stochasticcontrolshamiltoniansystemsandhjbequations |