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We present two examples of a large deviations principle where the ratefunction is not strictly convex. This is motivated by a model used inmathematical finance (the Heston model), and adds a new item to the zoology ofnon strictly convex large deviations. For one of these examples, we show thatthe rate function of the Cramer-type of large deviations coincides with that ofthe Freidlin-Wentzell when contraction principles are applied.

Two examples of non strictly convex large deviations