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Statistical Inference for Stochastic Differential Equations with Small Noises

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Listed:
  • Liang Shen
  • Qingsong Xu

Abstract

This paper proposes the least squares method to estimate the drift parameter for the stochastic differential equations driven by small noises, which is more general than pure jump α‐stable noises. The asymptotic property of this least squares estimator is studied under some regularity conditions. The asymptotic distribution of the estimator is shown to be the convolution of a stable distribution and a normal distribution, which is completely different from the classical cases.

Suggested Citation

  • Liang Shen & Qingsong Xu, 2014. "Statistical Inference for Stochastic Differential Equations with Small Noises," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:473681
    DOI: 10.1155/2014/473681
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    References listed on IDEAS

    as
    1. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(3), pages 365-383, December.
    2. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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