Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit behavior of the invariant measure for Langevin dynamics   In this manuscript, we consider the Langevin dynamics on $\mathbb{R}^d$ with
an overdamped vector field and driven by multiplicative Brownian noise of small
amplitude $\sqrt{\epsilon}$, $\epsilon>0$. Under suitable assumptions on the
vector field and the diffusion coefficient, it is well-known that it possesses
a unique invariant probability measure $\mu^{\epsilon}$. As $\epsilon$ tends to
zero, we prove that the probability measure $\epsilon^{d/2}
\mu^{\epsilon}(\sqrt{\epsilon}\mathrm{d} x)$ converges in the $p$-Wasserstein
distance for $p\in [1,2]$ to a Gaussian measure with zero-mean vector and
non-degenerate covariance matrix which solves a Lyapunov matrix equation.
Moreover, the error term is estimated. We emphasize that generically no
explicit formula for $\mu^{\epsilon}$ can be found.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph