Abstract
We consider stochastic reaction-diffusion equations with colored noise on the space of real-valued and continuous functions on a compact subset of ℝd for . We prove Schauder-type estimates, which will depend on the color of the noise, for the stationary and evolution problems associated with the corresponding transition semigroup.
Acknowledgments
The authors would like to express their gratitude to the anonymous referees for the meticulous review of the manuscript and for providing numerous valuable comments and suggestions that have significantly improved the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Fundings
The authors are members of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of the Italian Istituto Nazionale di Alta Matematica (INdAM).