2019
DOI: 10.48550/arxiv.1910.03543
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An Analysis of the Milstein Scheme for SPDEs without a Commutative Noise Condition

Abstract: In order to approximate solutions of stochastic partial differential equations (SPDEs) that do not possess commutative noise, one has to simulate the involved iterated stochastic integrals. Recently, two approximation methods for iterated stochastic integrals in infinite dimensions were introduced in [8]. As a result of this, it is now possible to apply the Milstein scheme by Jentzen and Röckner [2] to equations that need not fulfill the commutativity condition. We prove that the order of convergence of the Mi… Show more

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