For light-tailed Lévy bridges conditioned to hit x on short time scales, the sample path large deviation rate is an entropy functional whose unique minimizer is the linear path, with explicit jump-count and jump-increment asymptotics.
G.: Large Deviations for Stochastic Processes
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Large deviations for light-tailed L\'evy bridges on short time scales
For light-tailed Lévy bridges conditioned to hit x on short time scales, the sample path large deviation rate is an entropy functional whose unique minimizer is the linear path, with explicit jump-count and jump-increment asymptotics.