Malliavin calculus for stable processes on homogeneous groups

Piotr Graczyk

Studia Mathematica (1991)

  • Volume: 100, Issue: 3, page 183-205
  • ISSN: 0039-3223

Abstract

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Let μ t t > 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 μ t have smooth densities.

How to cite

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Graczyk, Piotr. "Malliavin calculus for stable processes on homogeneous groups." Studia Mathematica 100.3 (1991): 183-205. <http://eudml.org/doc/215882>.

@article{Graczyk1991,
abstract = {Let $\{μ_t\}_\{t>0\}$ 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 $μ_t$ have smooth densities.},
author = {Graczyk, Piotr},
journal = {Studia Mathematica},
keywords = {symmetric semigroup; stable measures; Malliavin calculus; smooth densities},
language = {eng},
number = {3},
pages = {183-205},
title = {Malliavin calculus for stable processes on homogeneous groups},
url = {http://eudml.org/doc/215882},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Graczyk, Piotr
TI - Malliavin calculus for stable processes on homogeneous groups
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 3
SP - 183
EP - 205
AB - Let ${μ_t}_{t>0}$ 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 $μ_t$ have smooth densities.
LA - eng
KW - symmetric semigroup; stable measures; Malliavin calculus; smooth densities
UR - http://eudml.org/doc/215882
ER -

References

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  12. [12] A. Janssen, Charakterisierung stetiger Faltungshalbgruppen durch das Lévy-Mass, Math. Ann. 246 (1980), 233-240. Zbl0407.60005
  13. [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. 
  14. [14] P. Pazy, Semi-groups of Linear Operators and Application to Partial Differential Equations, Springer, New York 1983. Zbl0516.47023
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  16. [16] F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, New York 1983. Zbl0516.58001

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