Title :

Asymptotic expansion for the quadratic variations of the solution to the heat equation with additive white noise

Author(s) :

Araya, Héctor [Auteur]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Stochastics and Dynamics

Pages :

2150010

Publisher :

World Scientific Publishing

Publication date :

2020-06-03

ISSN :

0219-4937

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We consider the sequence of spatial quadratic variations of the solution to the stochastic heat equation with space-time white noise. This sequence satisfies a Central Limit Theorem. By using Malliavin calculus, we refine ...
Show more >We consider the sequence of spatial quadratic variations of the solution to the stochastic heat equation with space-time white noise. This sequence satisfies a Central Limit Theorem. By using Malliavin calculus, we refine this result by proving the convergence of the sequence of densities and by finding the second-order term in the asymptotic expansion of the densities. In particular, our proofs are based on sharp estimates of the correlation structure of the solution, which may have their own interest.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL