Asymptotic behaviour of the density in a parabolic SPDE
AbstractConsider 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.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 371.
Date of creation: Apr 1999
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Web page: http://www.econ.upf.edu/
Malliavin Calculus; parabolic SPDE; large deviations; Taylor expansion of a density; exponential estimates of the tail probabilities; stochastic integration by parts formula;
Find related papers by JEL classification:
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-07-28 (All new papers)
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- Chenal, Fabien & Millet, Annie, 1997. "Uniform large deviations for parabolic SPDEs and applications," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 161-186, December.
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