Subject: large deviations | Gärtner-Ellis | Mathematics - Probability | math.PR | non-convex rate function | Statistics & Probability | 60F10 | stochastic processes | 0104 Statistics
We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of t... View more
 M. Abramowitz and I. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications, 1972.
 P. Baldi and L. Caramellino. General Freidlin-Wentzell large deviations and positive diffusions. Statistics & Probability Letters, 81: 1218-1229, 2011.
 B. Bercu, L. Coutin and N. Savy. Sharp large deviations for the fractional Ornstein-Uhlenbeck process. SIAM Theory of Probability and its Applications, 55: 575-610, 2011.
 B. Bercu, F. Gamboa and M. Lavielle. Sharp large deviations for Gaussian quadratic forms with applications. ESAIM PS, 4: 1-24, 2000.
 B. Bercu and A. Rouault, Sharp large deviations for the Ornstein-Uhlenbeck process, SIAM Theory of Probability and its Applications, 46: 1-19, 2002.
 W. Bryc. Large deviations by the asymptotic value method. Diffusion processes and related problems in analysis, 1. Boston: Birkhau¨ser, 1990.
 H. Comman. Differentiability-free conditions on the free-energy rate function implying large deviations Conuentes Mathematici, 1(2): 181-196, 2009.
 G. Conforti, S. De Marco and J-D. Deuschel On small-noise equations with degenerate limiting system arising from volatility models. Large Deviations and Asymptotic Methods in Finance. Springer Proceedings in Mathematics & Statistics, 110, 2015.
 H. Cr`amer. Sur un nouveau th´eor`eme-limite de la th´eorie des probabilit´es. Actualit´es Scientiques et Industrielles 736 523. Colloque Consacr´e `a la Th´eorie des Probabilit´es 3. Hermann, Paris, 1938.