{'fraction_non_alphanumeric': 0.0421455938697318, 'fraction_numerical': 0.007662835249042145, 'mean_word_length': 4.226666666666667, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Søren Asmussen : Terminal distributions of skipfree Markov additive processes with absorbtion

Let X be a Markov additive process with continuous paths and a finite background Markov process J so that X evolves as Brownian motion with drift r(i) and variance σ2(i) when J(t) = i. Assuming that J is eventually absorbed at some state a, the density f(x) of Z = X(ζ) is found where ζ is the absorbtion time. The form of f(x) is non-smooth at x = 0, but the distributions of Z+ and Z− are both of phase-type. The derivation involves concepts and results from fluctuation theory such as the Markov processes obtained by sampling J when X is at a relative maximum or minimum. The details are somewhat different for the fluid case where σ2(i) = 0 for all i and the Brownian case σ2(i) > 0.