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Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures.
Mathematical statistics and data analysis
John A. Rice · 1988
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Second-order discretization schemes of stochastic differential systems for the computation of the invariant law
Denis Talay · 1990
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Lectures on the coupling method
Torgny Lindvall · 1992
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Transportation cost for Gaussian and other product measures
M. Talagrand · 1996
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On Kolmogorov’s equations for finite-dimensional diffusions
N. V. Krylov · 1999
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Exact solutions to the transportation problem on the line
Robert J. McCann · 1999
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Coupling, stationarity, and regeneration
Hermann Thorisson · 2000
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Multilevel Monte Carlo methods
Stefan Heinrich · 2001
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Recursive computation of the invariant distribution of a diffusion
Damien Lamberton and Gilles Pages · 2002
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Transportation cost-information inequalities and applications to random dynamical systems and diffusions
H. Djellout, A. Guillin, and L. Wu · 2004
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Stochastic numerics for mathematical physics
Grigori Noah Milstein and Michael V. Tretyakov · 2004
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Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
Ahmed Kebaier · 2005
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Multilevel Monte Carlo path simulation
Michael B. Giles · 2008
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Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process
Fabien Panloup · 2008
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A random Euler scheme for Carathéodory differential equations
A. Jentzen and A. Neuenkirch · 2009
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Optimal transport
Cédric Villani · 2009
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Curvature, concentration and error estimates for Markov chain Monte Carlo
Aldéric Joulin and Yann Ollivier · 2010
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Reflection coupling and Wasserstein contractivity without convexity
Andreas Eberle · 2011
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Bayesian learning via stochastic gradient Langevin dynamics
Max Welling and Yee W. Teh · 2011
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Stochastic stability of differential equations
Rafail Khasminskii · 2012
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Ergodic approximation of the distribution of a stationary diffusion: rate of convergence
Gilles Pagès and Fabien Panloup · 2012
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Strong approximation of solutions of stochastic differential equations with time-irregular coefficients via randomized Euler algorithm
Pawel Przybylowicz and Pawel Morkisz · 2014
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Ergodicity of Approximate MCMC Chains with Applications to Large Data Sets
Natesh S. Pillai and Aaron Smith · 2014
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Langevin diffusions and the Metropolis-adjusted Langevin algorithm
Quantifying the accuracy of approximate diffusions and Markov chains
Jonathan H. Huggins and James Zou · 2017
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Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients
Raphael Kruse and Yue Wu · 2017
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The true cost of stochastic gradient Langevin dynamics
Tigran Nagapetyan, Andrew B. Duncan, Leonard Hasenclever, Sebastian J. Vollmer, Lukasz Szpruch, and Konstantinos Zygalakis · 2017
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Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis
Maxim Raginsky, Alexander Rakhlin, and Matus Telgarsky · 2017
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Convergence of Langevin MCMC in KL-divergence
Xiang Cheng and Peter Bartlett · 2018
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T. Xifara, C. Sherlock, S. Livingstone, S. Byrne, and M. Girolami · 2014
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Multilevel Monte Carlo methods
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High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm
Alain Durmus and Eric Moulines · 2016
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Reflection couplings and contraction rates for diffusions
Andreas Eberle · 2016
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Jack Gorham, Andrew B. Duncan, Sebastian J. Vollmer, and Lester Mackey · 2016
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Dejun Luo and Jian Wang · 2016
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Without-replacement sampling for stochastic gradient methods
Ohad Shamir · 2016
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Sharp Convergence Rates for Langevin Dynamics in the Nonconvex Setting
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