Uniform Decay and Equicontinuity for Normalized, Parameter Dependent, ITO Integrals

Let be a collection of continuous, continuous-time martingales such that for all t> 0, the associated increasing processes satisfy . We show that if grows with sufficiently fast, then uniformly in . An equicontinuity property for normalized, parameter dependent stochastic integrals follows. These results serve in the study of the maximum likelihood estimation problem, over unbounded sets, for diffusion processes