Asymptotic Behavior of the Density in a Parabolic SPDE

A. Kohatsu-Higa (), D. Márquez-Carreras () and M. Sanz-Solé ()
Additional contact information
A. Kohatsu-Higa: Universitat Pompeu Fabra
D. Márquez-Carreras: Universitat de Barcelona
M. Sanz-Solé: Universitat de Barcelona

Journal of Theoretical Probability, 2001, vol. 14, issue 2, 427-462

Abstract: Abstract Consider the density of the solution X(t, x) of a stochastic heat equation with small noise at a fixed t∈[0, T], x∈[0, 1]. In this paper we study the asymptotics of this density as the noise vanishes. 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 iterative local integration by parts formula is developed.

Keywords: Malliavin Calculus; parabolic stochastic partial differential equations; large deviations; asymptotics of densities; stochastic integration by parts formula (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1011163714298 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011163714298

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1011163714298

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().