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Nonparametric Estimation of Trend for Stochastic Processes Driven by G-Brownian Motion with Small Noise

Author

Listed:
  • Xuekang Zhang

    (Ministry of Education, Anhui Polytechnic University)

  • Shounian Deng

    (Ministry of Education, Anhui Polytechnic University)

  • Weiyin Fei

    (Ministry of Education, Anhui Polytechnic University)

Abstract

The present paper deals with the problem of nonparametric estimation of the trend for stochastic processes driven by G-Brownian motion with small noise. The consistency, the bound on the rate of convergence, and the asymptotic distribution of the nonparametric estimator are studied. Finally, a numerical example is given to verify our theoretical results.

Suggested Citation

  • Xuekang Zhang & Shounian Deng & Weiyin Fei, 2023. "Nonparametric Estimation of Trend for Stochastic Processes Driven by G-Brownian Motion with Small Noise," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-14, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10045-y
    DOI: 10.1007/s11009-023-10045-y
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    References listed on IDEAS

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    1. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    2. M. Mishra & B. Prakasa Rao, 2011. "Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 101-109, May.
    3. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    4. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    5. Sergio Albeverio & Francesco Cordoni & Luca Persio & Gregorio Pellegrini, 2019. "Asymptotic expansion for some local volatility models arising in finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 527-573, December.
    6. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    7. Peng, Shige & Zhou, Quan, 2020. "A hypothesis-testing perspective on the G-normal distribution theory," Statistics & Probability Letters, Elsevier, vol. 156(C).
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