@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}, publisher = {Soci\'et\'e math\'ematique de France}, number = {327}, year = {2009}, mrnumber = {2642353}, zbl = {1206.60056}, language = {en}, url = {http://www.numdam.org/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://www.numdam.org/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://www.numdam.org/item/AST_2009__327__69_0/ %G en %F AST_2009__327__69_0
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://www.numdam.org/item/AST_2009__327__69_0/
[1] Malliavin calculus for processes with jumps, Stochastics Monographs, vol. 2, Gordon and Breach Science Publishers, 1987. | MR | Zbl
, & -[2] Calcul des variations stochastique et processus de sauts", Z. Wahrsch. Verw. Gebiete 63 (1983), p. 147-235. | DOI | MR | Zbl
- "[3] Stochastic differential equations of jump type and Lévy processes in diffeomorphisms group", J. Math. Kyoto Univ. 25 (1985), p. 71-106. | DOI | MR | Zbl
& - "[4] Canonical SDE's based on semimartingales with spatial parameters. I. Stochastic flows of diffeomorphisms", Kyushu J. Math. 53 (1999), p. 265-300. | DOI | MR | Zbl
& , "[5] Stochastic differential equations and diffusion processes, second ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., 1989. | Zbl
& -[6] Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps", Stochastic Process. Appl. 116 (2006), p. 1743-1769. | DOI | MR | Zbl
& - "[7] On the smoothness of of solutions to of jump type", Int. J. Differ. Equ. Appl. 2 (2001), p. 141-197. | MR | Zbl
& - "[8] Option pricing under double exponential jump diffusion model", Management Science 50 (2004), p. 1178-1192. | DOI
& - "[9] Stochastic flows and stochastic differential equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, 1990. | MR | Zbl
-[10] Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms", in Real and stochastic analysis, Trends Math., Birkhäuser, 2004, p. 305-373. | DOI | MR | Zbl
, "[11] On square integrable martingales", Nagoya Math. J. 30 (1967), p. 209-245. | DOI | MR | Zbl
& - "[12] 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] Régularité de processus de sauts dégénérés", Ann. Inst. H. Poincaré Probab. Statist. 21 (1985), p. 125-146. | EuDML | Numdam | MR | Zbl
- "[14] Régularité de processus de sauts dégénérés. II", Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), p. 209-236. | EuDML | Numdam | MR | Zbl
, "[15] 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] Option pricing when underlying stock returns are discontinuous", J. Financial Economics 3 (1976), p. 125-144. | DOI | Zbl
- "[17] Simplified Malliavin calculus", in Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, 1986, p. 101-130. | DOI | EuDML | Numdam | MR | Zbl
- "[18] The Malliavin calculus and related topics, Probability and its Applications (New York), Springer, 1995. | DOI | MR | Zbl
-[19] On the existence of smooth densities for jump processes", Probab. Theory Related Fields 105 (1996), p. 481-511. | DOI | MR | Zbl
- "[20] Lévy processes and infinitely divisible distributions, Cambridge Univ. Press, 1999. | MR | Zbl
-