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info.json
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info.json
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{
"abstract": "We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the strongly log-concave case. This allows us to study in a unified way a number of different integrators proposed in the literature for the overdamped and underdamped Langevin dynamics. In addition, we analyze a novel splitting method for the underdamped Langevin dynamics which only requires one gradient evaluation per time step. Under an additional smoothness assumption on a $d$--dimensional strongly log-concave distribution with condition number $\\kappa$, the algorithm is shown to produce with an $\\mathcal{O}\\big(\\kappa^{5/4} d^{1/4}\\epsilon^{-1/2} \\big)$ complexity samples from a distribution that, in Wasserstein distance, is at most $\\epsilon>0$ away from the target distribution.",
"authors": [
"Jesus Maria Sanz-Serna",
"Konstantinos C. Zygalakis"
],
"emails": [
"jmsanzserna@gmail.com",
"k.zygalakis@ed.ac.uk"
],
"id": "21-0453",
"issue": 242,
"pages": [
1,
37
],
"title": "Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations",
"volume": 22,
"year": 2021
}