Large deviation estimate of transition densities for jump processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 179-222. 
@article{AIHPB_1997__33_2_179_0,
     author = {Ishikawa, Yasushi},
     title = {Large deviation estimate of transition densities for jump processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {179--222},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {2},
     year = {1997},
     mrnumber = {1443956},
     zbl = {0877.60055},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1997__33_2_179_0/}
}
TY  - JOUR
AU  - Ishikawa, Yasushi
TI  - Large deviation estimate of transition densities for jump processes
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1997
SP  - 179
EP  - 222
VL  - 33
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_1997__33_2_179_0/
LA  - en
ID  - AIHPB_1997__33_2_179_0
ER  - 
%0 Journal Article
%A Ishikawa, Yasushi
%T Large deviation estimate of transition densities for jump processes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1997
%P 179-222
%V 33
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_1997__33_2_179_0/
%G en
%F AIHPB_1997__33_2_179_0
Ishikawa, Yasushi. Large deviation estimate of transition densities for jump processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 179-222. http://archive.numdam.org/item/AIHPB_1997__33_2_179_0/

[1] V.I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, Berlin, 1978. | MR | Zbl

[2] R. Azencott, Grand deviations et applications, in Ecole d'Eté de Probabilités de Saint-Flour, VIII-1978 (P.L. Henneqin, ed.), Lecture Notes in Math., Vol. 774, Springer-Verlag, Berlin, 1980, pp. 1-176. | MR | Zbl

[3] C. Berg and G. Frost, Potential theory on locally compact Abelian groups, in Ergebnisse der Mathematik, Band 87, Springer-Verlag, Berlin-Heidelberg-New York, 1975. | MR | Zbl

[4] G. Ben Arous and R. Léandre, Dćroissance exponentielle du noyau de la chaleur sur la diagonale (II), Probab. Th. Rel. Fields, Vol. 90, 1991, pp. 377-402. | MR | Zbl

[5] K. Bichteler, J.-B. Gravereaux and J. Jacod, Malliavin Calculus for Processes with Jumps, Gordon and Breach Science Publishers, New York, 1987. | MR | Zbl

[6] J.-M. Bismut, Martingales, the Malliavin culculus and hypoellipticity under general Hörmander's conditions, Z. Wahrscheinlichkeitstheorie verw. Gebiete, Vol. 56, 1981, pp. 469-505. | MR | Zbl

[7] J.-M. Bismut, Calcul des variations stochastiques et processus de sauts, Z. Wahrsch. Verw. Gebiete, Vol. 63, 1983, pp. 147-235. | MR | Zbl

[8] J.-M. Bismut, Large deviation and the Malliavin calculus, in Progress in Mathematics, Vol. 45 (J. Coates and S. Helgason, eds.), Birkhäuser, Boston-Basel-Stuttgart, 1984. | MR | Zbl

[9] J.-M. Bismut, Jump processes and boundary processes, in Proceeding Taniguchi Symp., 1982 (K. Ito, ed.), North-Holland/Kinokuniya, Tokyo, 1984, pp. 53-104. | MR | Zbl

[10] L. Breiman, Probability, Classics in applied mathematics, SIAM, Philadelphia, 1992. | MR | Zbl

[11] H. Doss and P. Priouret, Petites perturbations de systèmes dynamiques avec réflexion, Seminaire de Proba. XVII, Lecture Notes in Math., Vol. 986, Springer-Verlag, Berlin, 1983, pp. 353-370. | Numdam | MR | Zbl

[12] S.N. Ethier and T.G. Kurtz, Markov Processes, John Wiley and Sons, New York, 1986. | MR | Zbl

[13] W.H. Fleming and H.M. Soner, Asymptotic expansion for Markov processes with Lévy generators, Applied Math. Opt., Vol 19, 1989, pp. 203-223. | MR | Zbl

[14] M.I. Freidlin and A.D. Ventcel, Random perturbation of dynamical system, Grundlehren der math. Wissenschaften, Band 260, Springer-Verlag, Berlin, 1984. | Zbl

[15] P. Graczyk, Malliavin calculus for stable processes on homogeneous groups, Studia Math., Vol. 100, 1991, pp. 183-205. | MR | Zbl

[16] Y. Ishikawa, On the lower bound of the density for jump processes in small time, Bull. Sc. math., Vol. 117, 1993, pp. 463-483. | MR | Zbl

[17] Y. Ishikawa, Asymptotic behavior of the transition density for jump-type processes in small time, Tohoku Math. J., Vol. 46, 1994, pp. 443-456. | MR | Zbl

[18] Y. Ishikawa, On the upper bound of the density for truncated stable processes in small time, Potential Analysis, to appear. | MR | Zbl

[19] J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Grundlehren der math. Wissenschaften, Band 288, Springer-Verlag, Berlin, 1987. | MR | Zbl

[20] S. Kusuoka, Theory and application of Malliavin calculus (in Japanese), Sugaku (Math. Soc. Japan), Vol. 41, 1989, pp. 154-165. | Zbl

[21] S. Kusuoka, Stochastic analysis as infinite dimensional analysis (in Japanese), Sugaku (Math. Soc. Japan), Vol. 45, 1994, pp. 289-298. | MR | Zbl

[22] R. Léandre, Densité en temps petit d'un processus de sauts, Séminaire de Proba., XXI, Lecture Notes in Math., Vol. 1297, Springer-Verlag, Berlin, 1987, pp. 81-99. | Numdam | MR | Zbl

[23] R. Léandre, Minoration en temps petit de la densité d'une diffusion dégénérée, J. Funct. Anal., Vol. 74, 1987, pp. 399-414. | MR | Zbl

[24] R. Léandre, Régularité de processus de sauts dégénérés (II), Ann. Inst. H. Poincaré Probabilités, Vol. 24, 1988, pp. 209-236. | Numdam | MR | Zbl

[25] R. Léandre, Applications quantitatives et geometriques du calcul de Malliavin, in Stochastic Analysis (M. Métivier and S. Watanabe, eds.), Lecture Notes in Math., Vol. 1322, Springer-Verlag, Berlin, 1988, pp. 109-133. | MR | Zbl

[26] R. Léandre and F. Russo, Estimation de Varadhan pour des diffusions à deux paramètres, Probab. Th. Rel. Fields, Vol. 84, 1990, pp. 429-451. | MR | Zbl

[27] R. Léandre, A simple proof for a large deviation theorem, Proceeding of Conference of D. Nualart. | Zbl

[28] J.-P. Lepeltier and B. Marchal, Problème des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel, Ann. Inst. H. Poincaré Probabilités, Vol. 12, 1976, pp. 43-103. | Numdam | MR | Zbl

[29] J. Lynch and J. Sethuraman, Large deviations for processes with independent increments, Ann. Prob., Vol. 15, 1987, pp. 610-627. | MR | Zbl

[30] J.R. Norris, Integration by parts for jump processes, in Séminaire de Proba., XXII (J. Azéma, P.A.Meyer and M. Yor, eds.), Lecture Notes in Math., Vol. 1321, Springer-Verlag, Berlin, 1988, pp. 271-315. | Numdam | MR | Zbl

[31 J.J. Prat, Résolution de l'équation de Schrödinger par intégration stochastique du champ magnétique, Probab. Th. Rel. Fields, Vol. 95, 1993, pp. 217-235. | MR | Zbl

[32] K. Sato, Additive Processes (in Japanese), Kinokuniya, Tokyo, 1990.

[33] J.M. Stoyanov, Counterexamples in Probability, John Wiley ans Sons, New York, 1987. | MR | Zbl

[34] S. Watanabe, Stochastic analysis and its application (in Japanese), Sugaku (Math. Soc. Japan), Vol. 42, 1990, pp. 97-110. | MR | Zbl