论文标题
离散观察到的扩散的非参数贝叶斯推断
Nonparametric Bayesian inference of discretely observed diffusions
论文作者
论文摘要
我们考虑了贝叶斯对漂移和扩散系数函数在随机微分方程中的贝叶斯推断的问题，并在其实现溶液实现的情况下进行了离散观察。我们给出了良好的条件和后验度量的稳定近似值。这些条件尤其允许具有无限支持的先验。我们的证明依赖于使用参数抛物线方程的参数方法明确构建过渡概率密度。然后，我们研究这些结果在推断出出生和死亡过程中的应用。
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and stable approximations of the posterior measure. These conditions in particular allow for priors with unbounded support. Our proof relies on the explicit construction of transition probability densities using the parametrix method for general parabolic equations. We then study an application of these results in inferring the rates of Birth-and-Death processes.
