Density in small time for Levy processes

Jean Picard

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 357-389
  • ISSN: 1292-8100

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Picard, Jean. "Density in small time for Levy processes." ESAIM: Probability and Statistics 1 (1997): 357-389. <http://eudml.org/doc/104239>.

@article{Picard1997,
author = {Picard, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {Lévy process; jump process; Wiener process; infinitely divisible law},
language = {eng},
pages = {357-389},
publisher = {EDP Sciences},
title = {Density in small time for Levy processes},
url = {http://eudml.org/doc/104239},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Picard, Jean
TI - Density in small time for Levy processes
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 357
EP - 389
LA - eng
KW - Lévy process; jump process; Wiener process; infinitely divisible law
UR - http://eudml.org/doc/104239
ER -

References

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  1. BICHTELER, K., GRAVEREAUX, J. B. and JACOD, J. ( 1987), Malliavin calculus for processes with jumps, Stochastics Monographs 2, Gordon and Breach. Zbl0706.60057MR1008471
  2. BISMUT, J. M. ( 1983), Calcul des variations stochastique et processus de sauts, Z. Wahrscheinlichkeitstheorie verw. Gebiete 63 147-235. Zbl0494.60082MR701527
  3. FREIDLIN, M. I. and WENTZELL, A. D. ( 1984), Random perturbations of dynamical systems, Springer. Zbl0522.60055MR722136
  4. ISHIKAWA, Y. ( 1993), On the lower bound of the density for jump processes in small time, Bull. Sc. Math., 2e série 117 463-483. Zbl0793.60096MR1245807
  5. ISHIKAWA, Y. ( 1994), Asymptotic behavior of the transition density for jump type processes in small time, Tôhoku Math. J. 46 443-456. Zbl0818.60074MR1301283
  6. ISHIKAWA, Y. ( 1995), Large deviation estimate of transition densities for jump processes, preprint. MR1443956
  7. LÉANDRE, R. ( 1987), Densité en temps petit d'un processus de sauts, in: Séminaire de Probabilités XXI, Lect. N. in Math. 1247, Springer. Zbl0616.60078MR941977
  8. PICARD, J. ( 1996), On the existence of smooth densities for jump processes, Probab. Theory Relat. Fields 105 481-511. Zbl0853.60064MR1402654
  9. RUBIN, H. ( 1967), Supports of convolutions of identical distributions, in: Proc. 5th Berkeley Symposium, Vol. II, Part 1, Univ. Calif. Press. Zbl0216.46201MR216578
  10. TUCKER, H. G. ( 1962), Absolute continuity of infinitely divisible distributions, Pacific J. Math. 12 1125-1129. Zbl0109.36503MR146868
  11. TUCKER, H. G. ( 1965), On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuous, Transactions A. M. S. 118 316-330. Zbl0168.39102MR182061
  12. YAMAZATO, M. ( 1994), Absolute continuity of transition probabilities of multidimensional processes with stationary independent increments, Theory Prob. 39 347-354. Zbl0831.60024MR1404692

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