TY - JOUR
T1 - Tempered infinitely divisible distributions and processes
AU - Bianchi, M. L.
AU - Rachev, S. T.
AU - Kim, Y. S.
AU - Fabozzi, F. J.
PY - 2011
Y1 - 2011
N2 - In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced in the seminal work of Rosi ́nski [Stochastic Process. Appl., 117 (2007), pp. 677-707], a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosínski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric examples.
AB - In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced in the seminal work of Rosi ́nski [Stochastic Process. Appl., 117 (2007), pp. 677-707], a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosínski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric examples.
KW - Stable distributions
KW - Tempered infinitely divisible distributions
KW - Tempered stable distributions
UR - http://www.scopus.com/inward/record.url?scp=79955539078&partnerID=8YFLogxK
U2 - 10.1137/S0040585X97984632
DO - 10.1137/S0040585X97984632
M3 - Article
AN - SCOPUS:79955539078
SN - 0040-585X
VL - 55
SP - 2
EP - 26
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
IS - 1
ER -