标题： 小噪声渐近下具有跳跃的随机微分方程的自适应贝叶斯估计量 显示英文标题

标题： Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics

摘要： 在本文中，我们考虑由维纳过程和复合泊松过程驱动的随机微分方程的参数估计。 我们假设与漂移项、扩散项和跳跃项系数相对应的未知参数，以及泊松强度和基础跳跃的概率密度函数。 我们基于离散观测的自适应贝叶斯估计提出估计量。 我们在小噪声渐近框架内证明了估计量的一致性和渐近正态性。 显示英文摘要

摘要： In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term, and jump term, as well as the Poisson intensity and the probability density function of the underlying jump. We propose estimators based on adaptive Bayesian estimation from discrete observations. We demonstrate the consistency and asymptotic normality of the estimators within the framework of small noise asymptotics.