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 Title: Asymptotic behaviour of the density in a parabolic SPDE Kohatsu, Arturo; Márquez Carreras, D.; Sanz Solé, M. Universitat Pompeu Fabra. Departament d'Economia i Empresa Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped. 2005-09-15 Statistics, Econometrics and Quantitative Methodsmalliavin calculusparabolic spdelarge deviationstaylor expansion of a densityexponential estimates of the tail probabilitiesstochastic integration by parts formula L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Working Paper

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