{'fraction_non_alphanumeric': 0.03398058252427184, 'fraction_numerical': 0.0024271844660194173, 'mean_word_length': 5.555555555555555, '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}}
Hypoelliptic stochastic differential equations in infinite dimensions

In [1], the author showed the absolute continuity of a measure induced by infinite dimensional stochastic differential equations of the type dXt = dWt + A(Xt)dWt + b(Xt)dt under the condition that the modified Malliavin covariance is non-degenerate. We give a sufficient condition for the non-degeneracy of the modified Malliavin covariance.