Objective
This ERC project addresses mathematical theories and numerical tools for mean-field models, which are used to describe the statistical state of a population. Mathematically, such models are often seen as time-dependent systems whose state variable takes values in a space of probability measures. One of the key features of the ERC project is its focus on mean field models for which the state of the population is itself random. Primarily, we aim to consider dynamics with values in the space of probability measures that are subject to an external noise, which is often called a common noise. Our main hypothesis may be formulated as follows: It is possible to construct a common noise that would force mean-field dynamics to explore the space of probability measures in an efficient manner, very much in the spirit of a Brownian motion in the Euclidean setting. This hypothesis will be studied along the following three axes: 1) Exploration is used for forcing uniqueness and stability of solutions to Fokker-Planck and related McKean-Vlasov equations and also to mean-field models of rational agents like mean-field control problems or mean-field games; 2) Exploration is used for the numerical analysis and the statistical learning of mean-field models featuring some optimisation criteria; 3) Exploration can be subject to a more irregular noise than a Brownian motion in the spirit of rough path theory. Expected applications are in probability theory, partial differential equations, control and game theory, optimisation, mathematical modelling and numerical methods at the interface with machine learning.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2021-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
06100 Nice
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.