Fractional constant elasticity of variance model

通过CKLS--CIR变换对小型噪声CEV型扩散的弹性估计

Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions

针对小噪声CEV型扩散，提出基于CKLS-CIR变换的两步弹性估计器，证明其一致性与中心极限定理，并通过辅助CIR过程转移极限理论。

Fractional Poisson random sum and its associated normal variance mixture

In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains the Poisson and geometric summations as particular cases. We show that the weak limit of the FP summation, when properly normalized, is a mixture between the normal and Mittag-Leffler distributions, which we call by Normal-Mittag-Leffler (NML) law. A parameter estimation procedure for the NML distribution is developed and the associated asymptotic distribution is derived. Simulations are performed to c…

带一般噪声的分数布朗运动的渐近效率

Asymptotic Efficiency for Fractional Brownian Motion with general noise

本文在统一框架下研究带高斯滑动平均噪声的分数布朗运动离散观测的局部渐近性质，证明 Hurst 指数估计的最优收敛速率并构造达到该速率和渐近有效方差的估计量，同时通过数值分析验证其有限样本有效性。

Hyperbolic decay time series

Hyperbolic decay time series such as, fractional Gaussian noise (FGN) or fractional autoregressive moving-average (FARMA) process, each exhibit two distinct types of behaviour: strong persistence or antipersistence. Beran (1994) characterized the family of strongly persistent time series. A more general family of hyperbolic decay time series is introduced and its basic properties are characterized in terms of the autocovariance and spectral density functions. The random shock and inverted form representations are derived. It is shown that every strongly persistent series is the dual of an anti…

从离散观测的积分方差估计随机波动率的粗糙度指数

Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance

本文提出一种基于离散观测积分方差的简单估计器，用于估计随机波动率过程的粗糙度指数，通过路径性分析证明其一致性，并展示其在粗糙波动模型中的应用。

基于保号分数幂基的信号参数多项式估计中的秩一方差膨胀

Rank-one variance inflation in polynomial estimation of signal parameters with a sign-preserving fractional-power basis

针对多项式最大化估计中噪声特性由残差估计导致精度损失的问题，推导出两步估计器渐近协方差的秩一增量闭式，并给出等价条件与实验验证。