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Stochastic interacting systems: Limiting Behavior, Evaluation, Regularity and Applications

Project description

Solving complex stochastic systems

Stochastic interacting systems, which model complex phenomena like neural networks, hydrodynamics, and financial markets, present intricate mathematical challenges. These systems often involve nonlinear equations with irregular coefficients and high-dimensionality, making them difficult to analyse and compute. Addressing these issues requires a multidisciplinary approach that spans stochastic differential equations, numerical simulation, and other advanced mathematical techniques. With the support of the Marie Skłodowska-Curie Actions programme, the LiBERA project tackles these challenges by uniting experts to explore the regularity and behaviour of solutions in such systems. By leveraging diverse methodologies, LiBERA aims to advance our understanding and practical applications of these models, while also training early career researchers for careers in both academia and industry.

Objective

This SE aims at addressing a number of challenging mathematical problems related to stochastic interacting systems, with particular emphasis on the regularity properties of the solutions, their limiting behaviour and numerical computation. The equations we analyse arise from the modelisation of real-world phenomena in several fields of application, including spiking neural systems, hydrodynamics and financial/energy markets, and share nonlinearity as a common underlying trait. Critically, nonlinearity intertwines with other relevant features that include: low regularity of the coefficients, noise degeneracy, jump-diffusion dynamics, and high-dimensionality.
The study of stochastic interacting systems is highly multidisciplinary from a two-fold perspective. On one hand, they have become a widespread modelling tool in a variety of applications. For example, they are used to model human neuron interfaces, particle systems, but also interacting agents in economics and finance, in relation to managing risk and decentralised production of renewable energy. On the other hand, the set of mathematical and computational tools needed to reach a holistic understanding of stochastic systems is very vast: ranging from stochastic (partial) differential equations, random measures, rough paths, gradient flows in metric measure spaces, numerical probability and computer simulation.
We provide a team of experts that analyse stochastic systems integrating several approaches and techniques. The complementary expertise across the network, together with the consolidated experience and excellence of the key participants in their research areas, places our network in the privileged position to make relevant contributions across interconnected research fields, and to contribute to the training of the early career researchers involved in the project in an exciting field of pure and applied mathematics, with the possibility of boosting their careers in both academic and non-academic sectors.

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Topic(s)

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HORIZON-TMA-MSCA-SE - HORIZON TMA MSCA Staff Exchanges

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Call for proposal

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(opens in new window) HORIZON-MSCA-2023-SE-01

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Coordinator

ALMA MATER STUDIORUM - UNIVERSITA DI BOLOGNA
Net EU contribution

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.

€ 312 800,00
Address
VIA ZAMBONI 33
40126 Bologna
Italy

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Region
Nord-Est Emilia-Romagna Bologna
Activity type
Higher or Secondary Education Establishments
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Total cost

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Participants (4)

Partners (14)

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