Department of Economics and Business - Universitat Pompeu Fabra

Title:: Asymptotic behaviour of the density in a parabolic SPDE
Authors:: Arturo Kohatsu, D. Márquez Carreras and M. Sanz Solé
Date:: April 1999
Abstract:: 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 noise parameter 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 approximating process and the limit one is proved. Also a suitable local integration by parts formula is developped.
Keywords:: Malliavin Calculus, parabolic SPDE, large deviations, Taylor expansion of a density, exponential estimates of the tail probabilities, stochastic integration by parts formula
JEL codes:: C15
Area of Research:: Statistics, Econometrics and Quantitative Methods
Published in:: Mathematics Preprint Series 257 of the Universitat de Barcelona and Journal of Theoretical Probability, 14, (2001), pp. 427-462

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