A large deviation principle is claimed for the slow variable in fully coupled slow-fast jump diffusions, with three different rate functions depending on the time-scale separation exponent.
Applebaum, L´ evy Processes and Stochastic Calculus
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Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian L\'evy noises
A large deviation principle is claimed for the slow variable in fully coupled slow-fast jump diffusions, with three different rate functions depending on the time-scale separation exponent.