{'fraction_non_alphanumeric': 0.01968503937007874, 'fraction_numerical': 0.001968503937007874, 'mean_word_length': 5.5256410256410255, '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}}
White Noise Approach to stochastic integration

We extend to white noise integrals the scalar type integrator inequalities introduced by Accardi, Fagnola and Quaegebeur [1] as a generalization of the Hudson–Parthasarathy basic estimates on stochastic integrals. We use these estimates as "regularity results", showing that some Hida distributions are in fact elements of the Fock space. We also use them to prove an analogue regularity result for solutions of white noise equations with bounded coefficients.