Young integrals and SPDEs

Massimiliano Gubinelli 1 Antoine Lejay 2, 3 Samy Tindel 2
3 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : In this note, we study the non-linear evolution problem dY_t = -A Y_t dt + B(Y_t) dX_t, where X is a \gamma-Hölder continuous function of the time parameter, with values in a distribution space, and -A the generator of an analytical semigroup. Then, we will give some sharp conditions on X in order to solve the above equation in a function space, first in the linear case (for any value of $\gamma$ in (0,1)), and then when B satisfies some Lipschitz type conditions (for \gamma>1/2). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type.
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Submitted on : Sunday, September 10, 2006 - 12:56:36 PM
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Massimiliano Gubinelli, Antoine Lejay, Samy Tindel. Young integrals and SPDEs. Potential Analysis, Springer Verlag, 2006, 25 (4), pp.307-326. ⟨inria-00092425⟩

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