For multidimensional Lévy processes with finite jump measure outside the Gaussian range, Hunt's hypothesis is equivalent to the same hypothesis holding for every one-dimensional projection, and new energy decay criteria are proved for products of independent processes.
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Hunt's Hypothesis (H) for Markov Processes: Survey and Beyond
For multidimensional Lévy processes with finite jump measure outside the Gaussian range, Hunt's hypothesis is equivalent to the same hypothesis holding for every one-dimensional projection, and new energy decay criteria are proved for products of independent processes.