Fundamental properties of process distances

Julio Backhoff Veraguas, Mathias Beiglböck, Manu Eder and Alois Pichler

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5575-5591

Abstract: To quantify the difference of distinct stochastic processes it is not sufficient to consider the distance of their states and corresponding probabilities. Instead, the information, which evolves and accumulates over time and which is mathematically encoded by filtrations, has to be accounted for as well. The nested distance, also known as bicausal Wasserstein distance, recognizes this component and involves the filtration properly. This distance is of emerging importance due to its applications in stochastic analysis, stochastic programming, mathematical economics and other disciplines.

Keywords: Optimal transport; Nested distance; Martingales; Causal Wasserstein distance; Information topology (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2020.03.017

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