by H. Duanmu, J.S. Rosenthal, and W. Weiss
Memoirs of the American Mathematical Society | 2019 (to appear)
Short Summary: Provides an alternative approach to proving convergence of Markov chains to stationary distributions, allowing for greater applicability including for more general MCMC algorithms.
by Soumik Pal and Ting-Kam Leonard Wong | 2018
Annals of Probability | Vol. 46, Number 2 (2018), 1070-1113
Short Summary: This paper uncovers deep connections between optimal transport and information geometry. It develops the dual geometry of L-divergence which extends the classical Bregman divergence. Our geometry can be applied to determine the optimal rebalancing frequency of portfolios.
Annals of Applied Probability | 2015 | Vol. 25(6), pp. 3592-3623
Short Summary: Provides a simple way to verify the correct convergence of adaptive MCMC algorithms, thus opening up new avenues for computational progress and accurate estimation.