TY - JOUR
T1 - The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component
AU - Buchmann, Boris
AU - Maller, Ross
PY - 2011/3
Y1 - 2011/3
N2 - We give a "small time" functional version of Chung's "other" law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
AB - We give a "small time" functional version of Chung's "other" law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
KW - Almost sure convergence
KW - Cluster sets
KW - Functional limit theorem
KW - Iterated logarithm laws
KW - Local behaviour
KW - Lévy process
KW - Other law of the iterated logarithm
UR - http://www.scopus.com/inward/record.url?scp=79952006766&partnerID=8YFLogxK
U2 - 10.1007/s00440-009-0255-1
DO - 10.1007/s00440-009-0255-1
M3 - Article
SN - 0178-8051
VL - 149
SP - 303
EP - 330
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 1
ER -