Given a separable and real Hilbert space H\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}$$\end{document} and a trace-class, symmetric and non-negative operator G:H→H\documentclass[12pt]{minimal}
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\begin{document}$$\mathscr {G}\,{:}\,{\mathbb {H}}\rightarrow {\mathbb {H}}$$\end{document}, we examine the equation dXt=-Xtdt+b(Xt)dt+2dWt,X0=x∈H,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} dX_t = -X_t dt + b(X_t) dt + \sqrt{2} dW_t, \quad X_0=x\in {\mathbb {H}}, \end{aligned}$$\end{document}where (Wt)\documentclass[12pt]{minimal}
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\begin{document}$$(W_t)$$\end{document} is a G\documentclass[12pt]{minimal}
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\begin{document}$$\mathscr {G}$$\end{document}-Wiener process on H\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}$$\end{document} and b:H→H\documentclass[12pt]{minimal}
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\begin{document}$$b\,{:}\,{\mathbb {H}}\rightarrow {\mathbb {H}}$$\end{document} is Lipschitz. We assume there is a splitting of H\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}$$\end{document} into a finite-dimensional space Hl\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}^l$$\end{document} and its orthogonal complement Hh\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}^h$$\end{document} such that G\documentclass[12pt]{minimal}
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\begin{document}$$\mathscr {G}$$\end{document} is strictly positive definite on Hl\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}^l$$\end{document} and the non-linearity b admits a contraction property on Hh\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}^h$$\end{document}. Assuming a geometric drift condition, we derive a Kantorovich (L1\documentclass[12pt]{minimal}
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\begin{document}$$L^1$$\end{document} Wasserstein) contraction with an explicit contraction rate for the corresponding Markov kernels. Our bounds on the rate are based on the eigenvalues of G\documentclass[12pt]{minimal}
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\begin{document}$$\mathscr {G}$$\end{document} on the space Hl\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {H}}^l$$\end{document}, a Lipschitz bound on b and a geometric drift condition. The results are derived using coupling methods.
