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Seminario di probabilità e finanza matematica: “Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation”

Martedì 14 Gennaio 2020, ore 11:00 - Aula 1BC50 - Richard C. Kraaij

ARGOMENTI: Seminari

Martedì 14 Gennaio 2020 alle ore 11:00 in Aula 1BC50, Richard C. Kraaij (Delft University of Technology) terrà un seminario dal titolo “Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation”.

Abstract
In statistical physics many interesting phenomena, e.g. behavior of systems at critical parameters or in the theory of hydrodynamic limits, arise from systems having multiple time-scales. A slow component is influenced by fast components, and as the number of interacting components tends to infinity, limiting results for the slow component are obtained in terms of `averaged' versions of the fast components.
I will consider in my talk the fluctuations (large deviations) of coupled Markovian systems with two-time scales. These fluctuations can arise from two sources: fluctuations of the slow process itself, or fluctuations of the large time averages of the fast process, effectively leading to a competition of two fluctuation effects. To obtain the large deviation principle, we consider an associated Hamilton-Jacobi-Bellman equation of which the Hamiltonian is given in terms of the two fluctuation effects. We establish under mild conditions that this Hamilton-Jacobi-Bellman equation is well-posed, and as a consequence that we have a large deviation principle for a wide class of weakly coupled Markov processes.
Based on joint work with Mikola Schlottke (Eindhoven, The Netherlands).