Geodesic
Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments
Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 45-68

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We extend the large deviation principles for random walks and processes with independent increments to the case of conditional probabilities given that the position of the trajectory at the last time moment is localized in a neighborhood of some point. As a corollary, we obtain a moderately large deviation principle for empirical distributions (an analog of Sanov's theorem). 
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     author = {A. A. Borovkov and A. A. Mogul'skiǐ},
     title = {Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments},
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     pages = {45--68},
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A. A. Borovkov; A. A. Mogul'skiǐ. Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments. Matematičeskie trudy, Tome 16 (2013) no. 2, pp. 45-68. http://geodesic.mathdoc.fr/item/MT_2013_16_2_a3/