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arXiv · 1308.4614

Finite difference schemes for stochastic partial differential equations in Sobolev spaces

Máté Gerencsér·István Gyöngy
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Abstract

We discuss $L_p$-estimates for finite difference schemes approximating parabolic, possibly degenerate, SPDEs, with initial conditions from $W^m_p$ and free terms taking values in $W^m_p.$ Consequences of these estimates include an asymptotic expansion of the error, allowing the acceleration of the approximation by Richardson's method.

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Máté Gerencsér, István Gyöngy. 2015-01-28. Finite difference schemes for stochastic partial differential equations in Sobolev spaces. https://doi.org/10.1007/s00245-014-9272-2

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