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Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

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  • Yuquan Cang
  • Junfeng Liu
  • Yan Zhang

Abstract

We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2), as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub‐fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub‐fractional Brownian motion.

Suggested Citation

  • Yuquan Cang & Junfeng Liu & Yan Zhang, 2014. "Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:635917
    DOI: 10.1155/2014/635917
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    References listed on IDEAS

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