Geodesic
Smooth density of canonical stochastic differential equation with jumps
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 69-91

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl 
Kunita, Hiroshi. Smooth density of canonical stochastic differential equation with jumps, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 69-91. http://geodesic.mathdoc.fr/item/AST_2009__327__69_0/
@incollection{AST_2009__327__69_0,
     author = {Kunita, Hiroshi},
     title = {Smooth density of canonical stochastic differential equation with jumps},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {69--91},
     year = {2009},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     mrnumber = {2642353},
     zbl = {1206.60056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AST_2009__327__69_0/}
}
TY  - CHAP
AU  - Kunita, Hiroshi
TI  - Smooth density of canonical stochastic differential equation with jumps
BT  - From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
AU  - Collectif
ED  - Dai Xianzhe
ED  - Léandre Rémi
ED  - Xiaonan Ma
ED  - Zhang Weiping
T3  - Astérisque
PY  - 2009
SP  - 69
EP  - 91
IS  - 327
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_2009__327__69_0/
LA  - en
ID  - AST_2009__327__69_0
ER  - 
%0 Book Section
%A Kunita, Hiroshi
%T Smooth density of canonical stochastic differential equation with jumps
%B From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
%A Collectif
%E Dai Xianzhe
%E Léandre Rémi
%E Xiaonan Ma
%E Zhang Weiping
%S Astérisque
%D 2009
%P 69-91
%N 327
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_2009__327__69_0/
%G en
%F AST_2009__327__69_0

[1] K. Bichteler, J.-B. Gravereaux & J. Jacod - Malliavin calculus for processes with jumps, Stochastics Monographs, vol. 2, Gordon and Breach Science Publishers, 1987. | MR | Zbl

[2] J.-M. Bismut - "Calcul des variations stochastique et processus de sauts", Z. Wahrsch. Verw. Gebiete 63 (1983), p. 147-235. | MR | Zbl | DOI

[3] T. Fujiwara & H. Kunita - "Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group", J. Math. Kyoto Univ. 25 (1985), p. 71-106. | MR | Zbl | DOI

[4] T. Fujiwara & H. Kunita, "Canonical SDE's based on semimartingales with spatial parameters. I. Stochastic flows of diffeomorphisms", Kyushu J. Math. 53 (1999), p. 265-300. | MR | Zbl | DOI

[5] N. Ikeda & S. Watanabe - Stochastic differential equations and diffusion processes, second ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., 1989. | Zbl

[6] Y. Ishikawa & H. Kunita - "Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps", Stochastic Process. Appl. 116 (2006), p. 1743-1769. | MR | Zbl | DOI

[7] T. Komatsu & A. Takeuchi - "On the smoothness of PDF of solutions to SDE of jump type", Int. J. Differ. Equ. Appl. 2 (2001), p. 141-197. | MR | Zbl

[8] S. G. Kou & J. Wang - "Option pricing under double exponential jump diffusion model", Management Science 50 (2004), p. 1178-1192. | DOI

[9] H. Kunita - Stochastic flows and stochastic differential equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, 1990. | MR | Zbl

[10] H. Kunita, "Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms", in Real and stochastic analysis, Trends Math., Birkhäuser, 2004, p. 305-373. | MR | Zbl | DOI

[11] H. Kunita & S. Watanabe - "On square integrable martingales", Nagoya Math. J. 30 (1967), p. 209-245. | MR | Zbl | DOI

[12] S. Kusuoka & D. Stroock - "Applications of the Malliavin calculus. I", in Stochastic analysis (Katata/Kyoto, 1982), North-Holland Math. Library, vol. 32, North-Holland, 1984, p. 271-306. | MR | Zbl

[13] R. Léandre - "Régularité de processus de sauts dégénérés", Ann. Inst. H. Poincaré Probab. Statist. 21 (1985), p. 125-146. | MR | Zbl | EuDML | Numdam

[14] R. Léandre, "Régularité de processus de sauts dégénérés. II", Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), p. 209-236. | MR | EuDML | Zbl | Numdam

[15] R. Léandre, "Malliavin calculus of Bismut type for Poisson processes without probability", to appear in the "Fractional systems", a special issue of Journal européen des systèmes automatisés, J. Sabatier et al. eds., 2008.

[16] R. Merton - "Option pricing when underlying stock returns are discontinuous", J. Financial Economics 3 (1976), p. 125-144. | Zbl | DOI

[17] J. Norris - "Simplified Malliavin calculus", in Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, 1986, p. 101-130. | MR | Zbl | EuDML | Numdam | DOI

[18] D. Nualart - The Malliavin calculus and related topics, Probability and its Applications (New York), Springer, 1995. | MR | Zbl | DOI

[19] J. Picard - "On the existence of smooth densities for jump processes", Probab. Theory Related Fields 105 (1996), p. 481-511. | MR | Zbl | DOI

[20] K. Sato - Lévy processes and infinitely divisible distributions, Cambridge Univ. Press, 1999. | MR | Zbl