Malliavin calculus for stable processes on homogeneous groups
Graczyk, Piotr
Studia Mathematica, Tome 100 (1991), p. 183-205 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let μtt>0 be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures μt have smooth densities.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:215882 
@article{bwmeta1.element.bwnjournal-article-smv100i3p183bwm,
     author = {Piotr Graczyk},
     title = {Malliavin calculus for stable processes on homogeneous groups},
     journal = {Studia Mathematica},
     volume = {100},
     year = {1991},
     pages = {183-205},
     zbl = {0745.60055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p183bwm}
}

Graczyk, Piotr. Malliavin calculus for stable processes on homogeneous groups. Studia Mathematica, Tome 100 (1991) pp. 183-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p183bwm/

[00000] [1] J.-M. Bismut, Calcul des variations stochastique et processus de sauts, Z. Wahrsch. Verw. Gebiete 63 (1983), 147-235. | Zbl 0494.60082

[00001] [2] J.-M. Bismut, Jump processes and boundary processes, in: Stochastic Analysis, Proc. Taniguchi Internat. Sympos., Katata and Kyoto, 1982, K. Itô (ed.), North-Holland Math. Library 32, Kinokuniya and North-Holland, 1984, 53-104.

[00002] [3] S. Ethier and T. Kurtz, Markov processes, Characterization and Convergence, Wiley, New York 1986. | Zbl 0592.60049

[00003] [4] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982. | Zbl 0508.42025

[00004] [5] I. I. Gikhman and A. W. Skorokhod, Introduction to the Theory of Stochastic Processes, Nauka, Moscow 1965 (in Russian).

[00005] [6] P. Głowacki, A calculus of symbols and convolution semigroups on the Heisenberg group, Studia Math. 77 (1982), 291-321. | Zbl 0504.43012

[00006] [7] P. Głowacki, Stable semigroups of measures on the Heisenberg group, ibid. 79 (1984), 105-138. | Zbl 0563.43002

[00007] [8] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups, Invent. Math. 83 (1986), 557-582. | Zbl 0595.43006

[00008] [9] A. Hulanicki, A class of convolution semi-groups of measures on a Lie group, in: Lecture Notes in Math. 828, Springer, 1980, 82-101. | Zbl 0462.28009

[00009] [10] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264-293. | Zbl 0073.12402

[00010] [11] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam 1981. | Zbl 0495.60005

[00011] [12] A. Janssen, Charakterisierung stetiger Faltungshalbgruppen durch das Lévy-Mass, Math. Ann. 246 (1980), 233-240. | Zbl 0407.60005

[00012] [13] P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, in: Proc. Internat. Sympos. on Stochastic Differential Equations, Kyoto 1976, K. Itô (ed.), Kinokuniya and Wiley, 1978, 195-263.

[00013] [14] P. Pazy, Semi-groups of Linear Operators and Application to Partial Differential Equations, Springer, New York 1983. | Zbl 0516.47023

[00014] [15] D. Stroock, The Malliavin calculus and its application to second order parabolic differential equations: Part I, Math. Systems Theory 14 (1981), 25-65. | Zbl 0474.60061

[00015] [16] F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, New York 1983. | Zbl 0516.58001