کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4614387 | 1339288 | 2016 | 22 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Weak error analysis for semilinear stochastic Volterra equations with additive noise Weak error analysis for semilinear stochastic Volterra equations with additive noise](/preview/png/4614387.png)
We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space–time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our convergence result concerns not only functionals of the solution at a fixed time but also more complicated functionals of the entire path and includes convergence of covariances and higher order statistics. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.
Journal: Journal of Mathematical Analysis and Applications - Volume 437, Issue 2, 15 May 2016, Pages 1283–1304