Malliavin calculus and asymptotic expansion for martingales

1997 ◽  
Vol 109 (3) ◽  
pp. 301-342 ◽  
Author(s):  
Nakahiro Yoshida
Keyword(s):  
Asymptotic Expansion ◽  
Malliavin Calculus

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

2020 ◽  
Vol 21 (02) ◽  
pp. 2150010
Author(s):  
Héctor Araya ◽  
Ciprian A. Tudor
Keyword(s):  
Asymptotic Expansion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Heat Equation ◽  
White Noise ◽  
Malliavin Calculus ◽  
Order Term ◽  
Sharp Estimates ◽  
Additive White Noise ◽  
Quadratic Variations

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.

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