Wasserstein error bounds for aggregations of continuous-time Markov chains

Fabian Michel

We study approximations of a finite continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds extend previous work on error bounds in the total variation distance. A Wasserstein matrix norm is used to bound the error caused by the lower-dimensional approximation of the dynamics. To control the propagation of the accumulated error, we rely on the concept of coarse Ricci curvature of a Markov chain. The practical applicability of the bounds depends strongly on the curvature of the chain. A running example demonstrates that positive curvature results in better bounds than those considered in previous works. In contrast, negative curvature results in exponentially exploding bounds.

Other talks in Q+F Session 1 - Markov Models under Uncertainty:

• Stationary and Transient Bounds for Nearly Lumpable or Uncertain Markov Chains
• Robust Parameter Learning for Uncertain MDPs

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