Divergence of an integral of a process with small ball estimate

Yuliya Mishura; Nakahiro Yoshida

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arXiv · 2102.01616

Divergence of an integral of a process with small ball estimate

Yuliya Mishura·Nakahiro Yoshida

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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 $\int_0^Tf(X_t)^2dt$ at the rate $T^{1-\epsilon}$ as $T\to\infty$ for every $\epsilon>0$. These conditions include so called small ball estimates which are discussed in detail. Statistical applications are provided.

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BibTeX RIS

Yuliya Mishura, Nakahiro Yoshida. 2021-02-02. Divergence of an integral of a process with small ball estimate. https://arxiv.org/abs/2102.01616

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