On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method

具有马尔可夫切换的遍历扩散过程的统计推断

Statistical inference for ergodic diffusion with Markovian switching

针对具有马尔可夫状态切换的遍历扩散过程，提出高斯拟似然参数估计方法，证明系数参数渐近正态并构造链生成元的一致估计量，仿真验证了理论结果。

Maximum Likelihood Estimator for Hidden Markov Models in continuous time

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions of the chain.

Estimating a periodicity parameter in the drift of a time inhomogeneous diffusion

We consider a diffusion $(ξ_t)_{t\ge 0}$ whose drift contains some deterministic periodic signal. Its shape being fixed and known, up to scaling in time, the periodicity of the signal is the unknown parameter $\vartheta$ of interest. We consider sequences of local models at $\vartheta$, corresponding to continuous observation of the process $ξ$ on the time interval $[0,n]$ as $n\to\infty$, with suitable choice of local scale at $\vartheta$. Our tools --under an ergodicity condition-- are path segments of $ξ$ corresponding to the period $\vartheta$, and limit theorems for certain functionals of…

Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models

We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function approach for a bivariate model, that is not a diffusion, but admits jumps. We do not use ergodicity arguments. We assume that both, logarithmic returns and instantaneous variance are observed on a discrete…

具有扩散驱动基线的Hawkes过程：长期行为、推断与统计检验

Hawkes process with a diffusion-driven baseline: long-run behavior, inference, statistical tests

本文提出了一种具有扩散驱动基线的Hawkes过程，通过动态适应外部协变量来捕捉自激发和外部影响，并建立了该过程的概率性质及推断方法。

Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the McKean-Vlasov SDE, and another in which we observe multiple particles from the interacting particle system. In each case, we begin by establishing consistency and asymptotic normality of the (approximate) offline maximum likelihood estimator, in the limit as the number of observations $N\rightarrow\infty$. We then propose an online maximum likelihood estimator, whi…