On LAN for parametrized continuous periodic signals in a time inhomogeneous diffusion

Multivariate inhomogeneous diffusion models with covariates and mixed effects

Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges parameter inference and approximations are inevitable. We propose a method for approximate maximum-likelihood parameter estimation in multivariate time-inhomogeneous diffusions, where subject-specific flexibility is accounted for by incorporation of multidimensional mixed effects and covariates. We consider $N$ multidimensional independent diffusions $X^i = (X…

Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion

We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $θ$. We prove Local Asymptotic Normality (LAN) jointly in $θ$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $θ$ or $T$ is assumed to be known.

Sampling normalizing constants in high dimensions using inhomogeneous diffusions

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on $\mathbb{R}^{d}$. The main results are nonasymptotic variance and bias bounds, and a central limit theorem in the $d\to\infty$ regime. We demonstrate that a temporal discretization inherits the fluctuation properties of the underlying diffusion, which are controlled at a computational cost growing at most polynomially with $d$. The key steps include establishing Poincaré …

时间非齐次预条件拉格朗日动力学

Time-Inhomogeneous Preconditioned Langevin Dynamics

本文提出TIPreL方法，通过时间与位置依赖的预条件器解决拉格朗日动力学在多模分布中的全局模式覆盖与局部模式探索问题，证明其在Wasserstein-2距离下的收敛性，并在实验中验证其有效性。