Monotone solutions for mean field games master equations: continuous state space and common noise
We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the...
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| Published in | Communications in partial differential equations Vol. 48; no. 10-12; pp. 1245 - 1285 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
02.12.2023
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0360-5302 1532-4133 |
| DOI | 10.1080/03605302.2023.2276564 |
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| Abstract | We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter. |
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| AbstractList | We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter. |
| Author | Bertucci, Charles |
| Author_xml | – sequence: 1 givenname: Charles surname: Bertucci fullname: Bertucci, Charles organization: CMAP, Ecole Polytechnique |
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| SubjectTerms | Analysis of PDEs Games Master equation Mathematical analysis Mathematics Mean Field Games Weak solutions |
| Title | Monotone solutions for mean field games master equations: continuous state space and common noise |
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