Publications: Probability

Ergodicity of Markov Processes via Non-Standard Analysis

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.

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Exponentially concave functions and a new information geometry

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.

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Stability of Adversarial Markov Chains, with an Application to Adaptive MCMC Algorithms

by R.V. Craiu, L. Gray, K. Latuszynski, N. Madras, G.O. Roberts, and J.S. Rosenthal

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.

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