Divergence of an integral of a process with small ball estimate

Abstract

The paper contains sufficient conditions on the function f and the stochastic process X that supply the rate of divergence of the integral functional T 0 f (X t ) 2 dt at the rate T 1−ǫ as T → ∞ for every ǫ > 0. These conditions include so called small ball estimates which are discussed in detail. Statistical applications are provided.