My bibliography  Save this paper

# Asymptotic behaviour of the density in a parabolic SPDE

## Author

Listed:
• Arturo Kohatsu
• D. Márquez Carreras
• M. Sanz Solé

## 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.

## Suggested Citation

• Arturo Kohatsu & D. Márquez Carreras & M. Sanz Solé, 1999. "Asymptotic behaviour of the density in a parabolic SPDE," Economics Working Papers 371, Department of Economics and Business, Universitat Pompeu Fabra.
• Handle: RePEc:upf:upfgen:371
as

File URL: https://econ-papers.upf.edu/papers/371.pdf
File Function: Whole Paper

## References listed on IDEAS

as
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.
Full references (including those not matched with items on IDEAS)

### Keywords

Malliavin Calculus; parabolic SPDE; large deviations; Taylor expansion of a density; exponential estimates of the tail probabilities; stochastic integration by parts formula;

### JEL classification:

• C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

### NEP fields

This paper has been announced in the following NEP Reports:

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:371. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.econ.upf.edu/ .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.