Least squares estimators for stochastic differential equations driven by small Lévy noises

Hongwei Long, Chunhua Ma, Yasutaka Shimizu

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function . σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when . ε→0 and . n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

    Original languageEnglish
    JournalStochastic Processes and their Applications
    DOIs
    Publication statusAccepted/In press - 2015 Oct 5

    Fingerprint

    Least Squares Estimator
    Stochastic Equations
    Differential equations
    Differential equation
    Moment Conditions
    Lipschitz condition
    Regularity Conditions
    Parameter estimation
    Parameter Estimation
    Rate of Convergence
    Simulation Study
    Coefficient
    Model

    Keywords

    • Asymptotic distribution
    • Consistency
    • Discrete observations
    • Least squares method
    • Parameter estimation
    • Primary
    • Secondary
    • Stochastic differential equations

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

    Cite this

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    abstract = "We study parameter estimation for discretely observed stochastic differential equations driven by small L{\'e}vy noises. We do not impose Lipschitz condition on the dispersion coefficient function . σ and any moment condition on the driving L{\'e}vy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when . ε→0 and . n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.",
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    T1 - Least squares estimators for stochastic differential equations driven by small Lévy noises

    AU - Long, Hongwei

    AU - Ma, Chunhua

    AU - Shimizu, Yasutaka

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    Y1 - 2015/10/5

    N2 - We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function . σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when . ε→0 and . n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

    AB - We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function . σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when . ε→0 and . n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

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    KW - Consistency

    KW - Discrete observations

    KW - Least squares method

    KW - Parameter estimation

    KW - Primary

    KW - Secondary

    KW - Stochastic differential equations

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