201 research outputs found
Weak convergence for a spatial approximation of the nonlinear stochastic heat equation
We find the weak rate of convergence of the spatially semidiscrete finite
element approximation of the nonlinear stochastic heat equation. Both
multiplicative and additive noise is considered under different assumptions.
This extends an earlier result of Debussche in which time discretization is
considered for the stochastic heat equation perturbed by white noise. It is
known that this equation has a solution only in one space dimension. In order
to obtain results for higher dimensions, colored noise is considered here,
besides white noise in one dimension. Integration by parts in the Malliavin
sense is used in the proof. The rate of weak convergence is, as expected,
essentially twice the rate of strong convergence.Comment: 19 page
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