{'fraction_non_alphanumeric': 0.04265402843601896, 'fraction_numerical': 0.004739336492890996, 'mean_word_length': 4.222222222222222, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, '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}}
DYNAMICAL PROPERTIES OF LÉVY PROCESSES IN LIE GROUPS

Let ϕt be a Levy process in a semisimple Lie group G of noncompact type regarded as a stochastic flow on a homogeneous space of G, called a G-flow. We will determine the Lyapunov exponents and the stable manifolds of ϕt, and the stationary points of an associated vector field. As examples, SL(d,R)-flows and SO(1,d)-flows on SO(d) and Sd - 1 are discussed in details.