Stochastic and Differential Games: Theory and Numerical Methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1999
|
| Schriftenreihe: | Annals of the International Society of Dynamic Games
4 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L. |
| Beschreibung: | 1 Online-Ressource (XVI, 381 p) |
| ISBN: | 9781461215929 9781461272083 |
| DOI: | 10.1007/978-1-4612-1592-9 |
Internformat
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| 490 | 1 | |a Annals of the International Society of Dynamic Games |v 4 | |
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Datensatz im Suchindex
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| author | Bardi, Martino |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1592-9 |
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| spelling | Bardi, Martino Verfasser aut Stochastic and Differential Games Theory and Numerical Methods edited by Martino Bardi, T. E. S. Raghavan, T. Parthasarathy Boston, MA Birkhäuser Boston 1999 1 Online-Ressource (XVI, 381 p) txt rdacontent c rdamedia cr rdacarrier Annals of the International Society of Dynamic Games 4 The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L. Mathematics Distribution (Probability theory) Game Theory, Economics, Social and Behav. Sciences Probability Theory and Stochastic Processes Mathematik Stochastisches Spiel (DE-588)4129289-3 gnd rswk-swf Differentialspiel (DE-588)4012253-0 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Stochastisches Spiel (DE-588)4129289-3 s 2\p DE-604 Differentialspiel (DE-588)4012253-0 s 3\p DE-604 Raghavan, T. E. S. Sonstige oth Parthasarathy, T. Sonstige oth Annals of the International Society of Dynamic Games 4 (DE-604)BV036597181 4 https://doi.org/10.1007/978-1-4612-1592-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bardi, Martino Stochastic and Differential Games Theory and Numerical Methods Annals of the International Society of Dynamic Games Mathematics Distribution (Probability theory) Game Theory, Economics, Social and Behav. Sciences Probability Theory and Stochastic Processes Mathematik Stochastisches Spiel (DE-588)4129289-3 gnd Differentialspiel (DE-588)4012253-0 gnd |
| subject_GND | (DE-588)4129289-3 (DE-588)4012253-0 (DE-588)4143413-4 |
| title | Stochastic and Differential Games Theory and Numerical Methods |
| title_auth | Stochastic and Differential Games Theory and Numerical Methods |
| title_exact_search | Stochastic and Differential Games Theory and Numerical Methods |
| title_full | Stochastic and Differential Games Theory and Numerical Methods edited by Martino Bardi, T. E. S. Raghavan, T. Parthasarathy |
| title_fullStr | Stochastic and Differential Games Theory and Numerical Methods edited by Martino Bardi, T. E. S. Raghavan, T. Parthasarathy |
| title_full_unstemmed | Stochastic and Differential Games Theory and Numerical Methods edited by Martino Bardi, T. E. S. Raghavan, T. Parthasarathy |
| title_short | Stochastic and Differential Games |
| title_sort | stochastic and differential games theory and numerical methods |
| title_sub | Theory and Numerical Methods |
| topic | Mathematics Distribution (Probability theory) Game Theory, Economics, Social and Behav. Sciences Probability Theory and Stochastic Processes Mathematik Stochastisches Spiel (DE-588)4129289-3 gnd Differentialspiel (DE-588)4012253-0 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Game Theory, Economics, Social and Behav. Sciences Probability Theory and Stochastic Processes Mathematik Stochastisches Spiel Differentialspiel Aufsatzsammlung |
| url | https://doi.org/10.1007/978-1-4612-1592-9 |
| volume_link | (DE-604)BV036597181 |
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