TY - JOUR

T1 - Asymptotic expansion for the quadratic variations of the solution to the heat equation with additive white noise

AU - Araya, Héctor

AU - Tudor, Ciprian A.

N1 - Funding Information:
C. T. acknowledges partial support from the Labex CEMPI (ANR-11-LABX-0007-01) and MATHAMSUD project SARC (19-MATH-06).
Publisher Copyright:
© 2021 World Scientific Publishing Company.

PY - 2021/3

Y1 - 2021/3

N2 - 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.

AB - 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.

KW - Asymptotic expansion

KW - Malliavin calculus

KW - central limit theorem

KW - fourth moment theorem

KW - quadratic variation

KW - stochastic heat equation

UR - http://www.scopus.com/inward/record.url?scp=85086276645&partnerID=8YFLogxK

U2 - 10.1142/S0219493721500106

DO - 10.1142/S0219493721500106

M3 - Article

AN - SCOPUS:85086276645

VL - 21

JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

SN - 0219-4937

IS - 2

M1 - 2150009

ER -