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A stochastic invariantization method for Itô stochastic perturbations of differential equations. (English) Zbl 1423.60089

Summary: In general, adding a stochastic perturbation to a differential equation possessing an invariant manifold destroys the invariance as far as the Itô formalism is used. In this article, we propose an invariantization method for perturbations in the Itô case which can be used to restore invariance. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. We discuss in particular previous results obtained by P. Étoré et al. [J. Differ. Equations 257, No. 6, 2115–2135 (2014; Zbl 1304.60035)].

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92B05 General biology and biomathematics
60J28 Applications of continuous-time Markov processes on discrete state spaces
65C30 Numerical solutions to stochastic differential and integral equations

Citations:

Zbl 1304.60035
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