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Malliavin calculus for Lévy processes with arbitrary Lévy measures
Author(s):
A.
M.
Kulik
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
75-92.
MSC (2000):
Primary 60H07;
Secondary 60G51
Posted:
August 18, 2006
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Additional information
Abstract:
A new method is proposed to prove the absolute continuity of distributions of solutions of stochastic differential equations with jumps. The method is based on the differentiation in time in the space of functionals of the Poisson point measure. In contrast to the known Bismut and Picard methods, our approach can be applied to point measures with arbitrary Lévy measures. We obtain sufficient conditions for the absolute continuity of the solutions expressed in terms of the coefficients of the equation; the conditions do not involve assumptions on properties of the Lévy measure.
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Additional Information:
A.
M.
Kulik
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya 3, Kiev 01601, Ukraine
Email:
kulik@imath.kiev.ua
DOI:
10.1090/S0094-9000-06-00666-1
PII:
S 0094-9000(06)00666-1
Keywords:
Malliavin calculus,
L\'evy process,
stratification method,
admissible time-stretching transformations
Received by editor(s):
19/MAR/2004
Posted:
August 18, 2006
Additional Notes:
Supported by the Ministry of Science and Education of Ukraine, Project # 01.07/103.
Copyright of article:
Copyright
2006,
American Mathematical Society
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