{'fraction_non_alphanumeric': 0.017094017094017096, 'fraction_numerical': 0.0, 'mean_word_length': 5.43956043956044, '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}}
Elimination of Fast Variables for a Class of Nonlinear Stochastic Dynamical Systems

A set of nonlinear stochastic differential equations (NSDE's) that describes a large class of nonlinear stochastic dynamical systems is studied. By virtue of the stochastic generalization of usual adiabatic approximation, we obtain the solution of equation for the fast variable, and obtain a closed equation for the slow variable. The statistical properties of the new stochastic variables occurred are studied. The formal NSDE's are treated in the Stratonovich sense and the Ito sense respectively.