Divergence of an integral of a process with small ball estimate

Yuliya Mishura; Nakahiro Yoshida

Divergence of an integral of a process with small ball estimate

Probability 2021-02-03 v1 Statistics Theory Statistics Theory

Authors: Yuliya Mishura , Nakahiro Yoshida

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.

Keywords

integral functional stochastic process divergence rate small ball estimates statistical applications

Cite

@article{arxiv.2102.01616,
  title  = {Divergence of an integral of a process with small ball estimate},
  author = {Yuliya Mishura and Nakahiro Yoshida},
  journal= {arXiv preprint arXiv:2102.01616},
  year   = {2021}
}

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