A probabilistic approach to classical solutions of the master equation for large population equilibria:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2022
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
Volume 280, Number 1379 (second of 8 numbers) |
| Schlagwörter: | |
| Abstract: | "We analyze a class of nonlinear partial differential equations (PDEs) defined on Rd P2pRdq, where P2pRdq is the Wasserstein space of probability measures on Rd with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we prove that their solution can be extended to arbitrary large intervals. These nonlinear PDEs arise in the recent developments in the theory of large population stochastic control. More precisely they are the so-called master equations corresponding to asymptotic equilibria for a large population of controlled players with mean-field interaction and subject to minimization constraints. The results in the paper are deduced by exploiting this connection. In particular, we study the differentiability with respect to the initial condition of the flow generated by a forward-backward stochastic system of McKean-Vlasov type. As a byproduct, we prove that the decoupling field generated by the forward-backward system is a classical solution of the corresponding master equation. Finally, we give several applications to meanfield games and to the control of McKean-Vlasov diffusion processes"-- |
| Beschreibung: | Includes bibliographical references |
| Umfang: | v, 123 Seiten Illustrationen |
| ISBN: | 9781470453756 |
Internformat
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| 100 | 1 | |a Chassagneux, Jean-François |d 1980- |0 (DE-588)1236207718 |4 aut | |
| 245 | 1 | 0 | |a A probabilistic approach to classical solutions of the master equation for large population equilibria |c Jean-François Chassagneux ; Dan Crisan ; François Delarue |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2022 | |
| 264 | 4 | |c © 2022 | |
| 300 | |a v, 123 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1379 (second of 8 numbers) | |
| 500 | |a Includes bibliographical references | ||
| 520 | 3 | |a "We analyze a class of nonlinear partial differential equations (PDEs) defined on Rd P2pRdq, where P2pRdq is the Wasserstein space of probability measures on Rd with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we prove that their solution can be extended to arbitrary large intervals. These nonlinear PDEs arise in the recent developments in the theory of large population stochastic control. More precisely they are the so-called master equations corresponding to asymptotic equilibria for a large population of controlled players with mean-field interaction and subject to minimization constraints. The results in the paper are deduced by exploiting this connection. In particular, we study the differentiability with respect to the initial condition of the flow generated by a forward-backward stochastic system of McKean-Vlasov type. As a byproduct, we prove that the decoupling field generated by the forward-backward system is a classical solution of the corresponding master equation. Finally, we give several applications to meanfield games and to the control of McKean-Vlasov diffusion processes"-- | |
| 653 | 0 | |a Stochastic analysis | |
| 653 | 0 | |a Stochastic control theory | |
| 653 | 0 | |a Systems theory; control -- Stochastic systems and control -- Optimal stochastic control | |
| 653 | 0 | |a Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.) | |
| 653 | 0 | |a Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory | |
| 700 | 1 | |a Crisan, Dan |0 (DE-588)138298084 |4 aut | |
| 700 | 1 | |a Delarue, François |d 1976- |0 (DE-588)1156345413 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-7279-5 |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1379 (second of 8 numbers) |w (DE-604)BV008000141 |9 1379 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034058805 | |
Datensatz im Suchindex
| _version_ | 1818990288850386944 |
|---|---|
| any_adam_object | |
| author | Chassagneux, Jean-François 1980- Crisan, Dan Delarue, François 1976- |
| author_GND | (DE-588)1236207718 (DE-588)138298084 (DE-588)1156345413 |
| author_facet | Chassagneux, Jean-François 1980- Crisan, Dan Delarue, François 1976- |
| author_role | aut aut aut |
| author_sort | Chassagneux, Jean-François 1980- |
| author_variant | j f c jfc d c dc f d fd |
| building | Verbundindex |
| bvnumber | BV048684498 |
| ctrlnum | (OCoLC)1365560334 (DE-599)KXP1832134199 |
| dewey-full | 519.2/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/2 |
| dewey-search | 519.2/2 |
| dewey-sort | 3519.2 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV048684498 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T19:52:00Z |
| institution | BVB |
| isbn | 9781470453756 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034058805 |
| oclc_num | 1365560334 |
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| owner_facet | DE-29T DE-83 DE-355 DE-BY-UBR DE-11 |
| physical | v, 123 Seiten Illustrationen |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Chassagneux, Jean-François 1980- (DE-588)1236207718 aut A probabilistic approach to classical solutions of the master equation for large population equilibria Jean-François Chassagneux ; Dan Crisan ; François Delarue Providence, RI American Mathematical Society 2022 © 2022 v, 123 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society Volume 280, Number 1379 (second of 8 numbers) Includes bibliographical references "We analyze a class of nonlinear partial differential equations (PDEs) defined on Rd P2pRdq, where P2pRdq is the Wasserstein space of probability measures on Rd with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we prove that their solution can be extended to arbitrary large intervals. These nonlinear PDEs arise in the recent developments in the theory of large population stochastic control. More precisely they are the so-called master equations corresponding to asymptotic equilibria for a large population of controlled players with mean-field interaction and subject to minimization constraints. The results in the paper are deduced by exploiting this connection. In particular, we study the differentiability with respect to the initial condition of the flow generated by a forward-backward stochastic system of McKean-Vlasov type. As a byproduct, we prove that the decoupling field generated by the forward-backward system is a classical solution of the corresponding master equation. Finally, we give several applications to meanfield games and to the control of McKean-Vlasov diffusion processes"-- Stochastic analysis Stochastic control theory Systems theory; control -- Stochastic systems and control -- Optimal stochastic control Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.) Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory Crisan, Dan (DE-588)138298084 aut Delarue, François 1976- (DE-588)1156345413 aut Erscheint auch als Online-Ausgabe 978-1-4704-7279-5 Memoirs of the American Mathematical Society Volume 280, Number 1379 (second of 8 numbers) (DE-604)BV008000141 1379 |
| spellingShingle | Chassagneux, Jean-François 1980- Crisan, Dan Delarue, François 1976- A probabilistic approach to classical solutions of the master equation for large population equilibria Memoirs of the American Mathematical Society |
| title | A probabilistic approach to classical solutions of the master equation for large population equilibria |
| title_auth | A probabilistic approach to classical solutions of the master equation for large population equilibria |
| title_exact_search | A probabilistic approach to classical solutions of the master equation for large population equilibria |
| title_full | A probabilistic approach to classical solutions of the master equation for large population equilibria Jean-François Chassagneux ; Dan Crisan ; François Delarue |
| title_fullStr | A probabilistic approach to classical solutions of the master equation for large population equilibria Jean-François Chassagneux ; Dan Crisan ; François Delarue |
| title_full_unstemmed | A probabilistic approach to classical solutions of the master equation for large population equilibria Jean-François Chassagneux ; Dan Crisan ; François Delarue |
| title_short | A probabilistic approach to classical solutions of the master equation for large population equilibria |
| title_sort | a probabilistic approach to classical solutions of the master equation for large population equilibria |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT chassagneuxjeanfrancois aprobabilisticapproachtoclassicalsolutionsofthemasterequationforlargepopulationequilibria AT crisandan aprobabilisticapproachtoclassicalsolutionsofthemasterequationforlargepopulationequilibria AT delaruefrancois aprobabilisticapproachtoclassicalsolutionsofthemasterequationforlargepopulationequilibria |