Lower functions for processes with stationary independent increments

Summary Let {X _t } be aR ¹-valued process with stationary independent increments and . In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infA _t /h(t)=C a.s. ast0 andt, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.This research is partially supported by Korea Science & Engineering Foundation     

Moderate deviations and functional limits for random processes with stationary and independent increments

We first give a functional moderate deviation principle for random processes with stationary and independent increments under the Ledoux's condition. Then we apply the result to the functional limits for increments of the processes and obtain some Csorgo-Revesz type functional laws of the iterated logarithm.     

Stochastic integrators with stationary independent increments

Summary Lipschitzian stochastic differential equations driven by a process with stationary independent increments permit a priori growth and stability estimates up to any sure time, and the solutions depend differentiably on parameters provided the Levy measure of the driving term has suitable moments.Research partially supported by NSF grant Nr. MCS 8001779