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Derivatives of local times for some Gaussian fields II

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  • Hong, Minhao
  • Xu, Fangjun

Abstract

Given a (2,d)-Gaussian field Z={Z(t,s)=XtH1−X˜sH2,s,t≥0},where XH1 and X˜H2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈Rd, this condition is also sufficient when XH1 and X˜H2 satisfy the local nondeterminism property.

Suggested Citation

  • Hong, Minhao & Xu, Fangjun, 2021. "Derivatives of local times for some Gaussian fields II," Statistics & Probability Letters, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:stapro:v:172:y:2021:i:c:s0167715221000250
    DOI: 10.1016/j.spl.2021.109063
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Song, Jian & Xu, Fangjun & Yu, Qian, 2019. "Limit theorems for functionals of two independent Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4791-4836.
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