This work aims at making a comprehensive contribution in the general area of parametric inference for partially observed diffusion processes. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) model over finite time periods. The scheme is applied for a step-size that is either a user-selected tuning parameter or determined by the data. Recent research has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates in the setting of hypo-elliptic SDEs. In brief, in our work, first, we develop two weak second order `sampling schemes' (to cover both the hypo-elliptic and elliptic SDE classes) and generate accompanying `transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods. We present numerical results from carrying out classical or Bayesian inference, for both elliptic and hypo-elliptic SDE models.
翻译:这项工作旨在为部分观测到的传播过程的参数推断这一总体领域做出全面贡献。基于可能性的既定估算方法,在一定的时期内,为Stochatical diffarial Equation (SDE) 模型的近似(通常难以处理的)过渡动态,援引一个数字时间分解办法,以近似于(SDE) 定时的(SDE) 模型的过渡动态。这个办法用于一个由用户选择的调整参数或由数据决定的阶梯尺寸。最近的研究突出了数字方法的选择对确定低等离子 SDE 的衍生参数估计行为所产生的关键影响。简而言之,我们在工作中,首先,我们开发了两个薄弱的第二顺序“抽样办法”(涵盖低利和椭圆 SDE 类),并同时产生SDE 的“过渡密度计划”(即SDE 转换为SDE ) 。然后,我们收集了分析结果,提供一个完整的理论框架,以巩固所拟议的计划,并展示其纳入SDE elcirgition 方法的优势。我们介绍了从执行古典或Bayal-al-servial模型的数值模型取得的结果。