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Quantitative approximation of a Keller--Segel PDE by a branching moderately interacting particle system and suppression of blow-up
Thomas Cavallazzi, Alexandre Richard, Milica Tomasevic
The Keller--Segel PDE is a model for chemotaxis known to exhibit possible finite-time blow-up. Following a seminal work by Tello and Winkler, a logistic damping term is added in th…
Well-posedness and propagation of chaos for L{é}vy-driven McKean-Vlasov SDEs under Lipschitz assumptions
Thomas Cavallazzi
The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by L{é}vy processes on having a finite moment of order an…
It{ô}'s formula for the flow of measures of Poisson stochastic integrals and applications
Thomas Cavallazzi
We prove It{ô}'s formula for the flow of measures associated with a jump process defined by a drift, an integral with respect to a Poisson random measure and with respect to the as…
Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential
Thomas Cavallazzi, Emeline Luirard
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is so…