Divergence of an integral of a process with small ball estimate

02/02/2021

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by   Yuliya Mishura, et al.

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The paper contains sufficient conditions on the function f and the stochastic process X that supply the rate of divergence of the integral functional ∫_0^Tf(X_t)^2dt at the rate T^1-ϵ as T→∞ for every ϵ>0. These conditions include so called small ball estimates which are discussed in detail. Statistical applications are provided.