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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.
Statistics, Econometrics and Quantitative Methods
malliavin calculus
parabolic spde
large deviations
taylor expansion of a density
exponential estimates of the tail probabilities
stochastic integration by parts formula
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