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Divergence of an integral of a process with small ball estimate

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  • Mishura, Yuliya
  • Yoshidae, Nakahiro

Abstract

The paper contains sufficient conditions on the function f and the stochastic process X that supply the divergence of the integral functional ∫0Tf(Xt)2dt at the rate T1−ε as T→∞ for every ε>0. These conditions include so called small ball estimates which are discussed in detail. Statistical applications are provided.

Suggested Citation

  • Mishura, Yuliya & Yoshidae, Nakahiro, 2022. "Divergence of an integral of a process with small ball estimate," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 1-24.
    • Handle: RePEc:eee:spapps:v:148:y:2022:i:c:p:1-24
    DOI: 10.1016/j.spa.2022.02.006
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    References listed on IDEAS

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    1. Sabzikar, Farzad & Surgailis, Donatas, 2018. "Tempered fractional Brownian and stable motions of second kind," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 17-27.
    2. Mishura, Yuliya & Shevchenko, Georgiy, 2017. "Small ball properties and representation results," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 20-36.
    3. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    4. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    5. Ben-Ari, Iddo & Pinsky, Ross G., 2005. "Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 179-206, February.
    Full references (including those not matched with items on IDEAS)

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