A basic identity for Kolmogorov operators in the space of continuous functions related to RDEs with multiplicative noise∗
نویسندگان
چکیده
We consider the Kolmogorov operator associated with a reaction-diffusion equation having polynomially growing reaction coefficient and perturbed by a noise of multiplicative type, in the Banach space E of continuous functions. By analyzing the smoothing properties of the associated transition semigroup, we prove a modification of the classical identité du carré des champs that applies to the present non-Hilbertian setting. As an application of this identity, we construct the Sobolev space W (E;μ), where μ is an invariant measure for the system, and we prove the validity of the Poincaré inequality and of the spectral gap.
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