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math.PR2026
Strong Feller property, irreducibility, and uniqueness of the invariant measure for stochastic PDEs with degenerate multiplicative noise
Luca Scarpa, Margherita Zanella
We establish strong Feller property and irreducibility for the transition semigroup associated to a class of nonlinear stochastic partial differential equations with multiplicative…
math.PR2026
An Allen-Cahn equation with jump-diffusion noise for biological damage and repair processes
Andrea Di Primio, Marvin Fritz, Luca Scarpa +1
This paper analyzes a stochastic Allen--Cahn equation for the dynamics of biomolecular damage and repair. The system is driven by two distinct noise processes: a multiplicative cyl…