Spiking and collapsing in classical and quantum filtering

par Reda Chhaibi (Université Paul Sabatier Toulouse)

jeudi 15 févr. 2024, 14:00 → 15:00 Europe/Paris

Lyon 1

Recently, physicists Bernard, Tilloy and Bauer pointed out an intriguing phenomenon

in SDEs arising from the filtering of quantum open systems, in the strong noise regime.

On simulations, one notices that these trajectories of SDEs "locally" collapse to a Markov jump process.
 

Yet trajectories are decorated by "spikes" which are very thin excursions.
 

In fact, the same SDEs appear in the classical context.
 

We will present several results obtained in various works with Benoist, Bernardin, Chetrite, Najnudel and Pellegrini.
 

- The mathematical description of "local collapse" and "spiking" which is complete in dim 1, and partial in dim \geq 2.

- A phrase transition in the smoothing of filters, depending on the smoothing window.