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On Optimal Markovian Couplings of Levy Processes
Wei Yang Kang, Tau Shean Lim
https://arxiv.org/abs/2509.23086 https://arxiv.org/pdf/2509.23086

On Optimal Markovian Couplings of Levy Processes
We study the optimal Markovian coupling problem for two Pi-valued Feller processes {X_t} and {Y_t}, which seeks a coupling process {(X_t, Y_t)} that minimizes the right derivative at t = 0 of the expected cost E^{(x,y)}[c(X_t, Y_t)], for all initial states (x,y) in Pi^2 and a given cost function c on Pi. This problem was first formulated and solved by Chen (1994) for drift-diffusion processes and later extended by Zhang (2000) to Markov processes with bounded jumps. In this work, we resolve the…

As I head out the door to attend my local Remembrance Day ceremony, here is a story from the CBC about the USA and Canada in WWII.
““We each share a border. If something happened to Canada tomorrow, wouldn't I want the United States to defend them? If something happened to us, wouldn't we want Canada to help defend us? So I'm telling you, we need as countries to resolve these issues that we are having right now, today.””
#canada #usa #wwii #veteransday #remembranceDay
https://www.cbc.ca/news/canada/british-columbia/canada-wwii-victoria-cross-9.6971182