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Asymptotic behaviour of the density in a parabolic SPDE

Listed author(s):
  • Arturo Kohatsu
  • D. Márquez Carreras
  • M. Sanz Solé
Registered author(s):

    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.

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    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 371.

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    Date of creation: Apr 1999
    Handle: RePEc:upf:upfgen:371
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    1. 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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