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Some limit theorems for fractional Lévy Brownian fields

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  • Lin, Zheng Yan
  • Choi, Yong-Kab

Abstract

In this paper we establish large increment results and moduli of continuty for a two-parameter fractional Lévy Brownian motion on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter fractional Lévy Brownian motion.

Suggested Citation

  • Lin, Zheng Yan & Choi, Yong-Kab, 1999. "Some limit theorems for fractional Lévy Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 229-244, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:229-244
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    References listed on IDEAS

    as
    1. Ortega, Joaquín, 1984. "On the size of the increments of nonstationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 47-56, September.
    2. Zhang, Li-Xin, 1996. "Two different kinds of liminfs on the LIL for two-parameter Wiener processes," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 175-188, November.
    3. El-Nouty, Charles, 1993. "A Hanson-Russo-type law of the iterated logarithm for fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 17(1), pages 27-34, May.
    4. Lacey, Michael T., 1989. "A remark on the multiparameter law of the iterated logarithm," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 355-367, August.
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    Cited by:

    1. Moon, Hee-Jin & Choi, Yong-Kab, 2015. "Berry–Esseen type theorems and the uniform law of the iterated logarithm for LPQD processes," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 191-198.
    2. Yong-Kab Choi, 2004. "Path properties of (N;d)-Gaussian random fields," RePAd Working Paper Series lrsp-TRS393, Département des sciences administratives, UQO.
    3. Yong-Kab Choi & Hwa-Sang Sung & Kyo-Shin Hwang & Hee-Jin Moon, 2004. "On the Csorgo-Révész increments of finite dimensional Gaussian random fields," RePAd Working Paper Series lrsp-TRS395, Département des sciences administratives, UQO.
    4. Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.

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