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Higher-order derivative of local times for space–time anisotropic Gaussian random fields

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  • Chen, Zhenlong
  • Xu, Peng

Abstract

Let X={X(t),t∈RN} be a centered space–time anisotropic Gaussian random field values in Rd. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of X(t) are studied. Moreover, we show that the derivatives of the local time of X(t) is jointly continuous on Rd×[0,1]N. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.

Suggested Citation

  • Chen, Zhenlong & Xu, Peng, 2024. "Higher-order derivative of local times for space–time anisotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001664
    DOI: 10.1016/j.spl.2024.110197
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    References listed on IDEAS

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    1. Jingjun Guo & Yaozhong Hu & Yanping Xiao, 2019. "Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1190-1201, September.
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    3. Kremer, D. & Scheffler, H.-P., 2019. "Operator-stable and operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4082-4107.
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    5. Peter Imkeller & Ferenc Weisz, 1999. "Critical Dimensions for the Existence of Self-Intersection Local Times of the N-Parameter Brownian Motion in R d," Journal of Theoretical Probability, Springer, vol. 12(3), pages 721-737, July.
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    Full references (including those not matched with items on IDEAS)

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