TY - JOUR
T1 - Stability equations for processes with stationary independent increments using branching processes and Poisson mixtures
AU - Harn, van, K.
AU - Steutel, F.W.
PY - 1993
Y1 - 1993
N2 - The equation X1 X2 W( X1+ X2)with W uniform (0,1) distributed and W,X1 and X2 independent, is generalized in several directions. Most importantly, a generalized multiplication operation is used in which subcritical branching processes, both with discrete and continuous state space, play an important role. The solutions of the equations so obtained are related to the concepts of self-decomposability and stability, both in the classical and in an extended sense. The solutions for +-valued random variables are obtained from those for +-valued random variables by way of Poisson mixtures. There are also some new results on (generalized) unimodality.
AB - The equation X1 X2 W( X1+ X2)with W uniform (0,1) distributed and W,X1 and X2 independent, is generalized in several directions. Most importantly, a generalized multiplication operation is used in which subcritical branching processes, both with discrete and continuous state space, play an important role. The solutions of the equations so obtained are related to the concepts of self-decomposability and stability, both in the classical and in an extended sense. The solutions for +-valued random variables are obtained from those for +-valued random variables by way of Poisson mixtures. There are also some new results on (generalized) unimodality.
U2 - 10.1016/0304-4149(93)90070-K
DO - 10.1016/0304-4149(93)90070-K
M3 - Article
SN - 0304-4149
VL - 45
SP - 209
EP - 230
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -