相关论文: Examples of moderate deviation principle for diffu…

We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…

Let $M$ be a $d$-dimensional connected compact Riemannian manifold with boundary $\partial M$, let $V\in C^2(M)$ such that $\mu(dx):=e^{V(x)} d x$ is a probability measure, and let $X_t$ be the diffusion process generated by…

Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two…

We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…

By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with…

We present new connections among anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem. This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by…

We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…

In this work, we study discrete minimizers of the Ginzburg-Landau energy in finite element spaces. Special focus is given to the influence of the Ginzburg-Landau parameter $\kappa$. This parameter is of physical interest as large values can…

The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fd\omega$ relies on independent samples from $\omega$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive…

The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…

This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…

Photon-counting computed tomography (PCCT) has emerged as a promising imaging technique, enabling spectral imaging and material decomposition (MD). However, images typically suffer from a low signal-to-noise ratio (SNR) due to constraints…

Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…

Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are…

We consider $\mathbb{R}^d$-valued diffusion processes of type \begin{align*} dX_t\ =\ b(X_t)dt\, +\, dB_t. \end{align*} Assuming a geometric drift condition, we establish contractions of the transitions kernels in Kantorovich ($L^1$…

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…

We study one-dimensional multi-particle Diffusion Limited Aggregation (MDLA) at its critical density $\lambda=1$. Previous works have verified that the size of the aggregate $X_t$ at time $t$ is $t^{1/2}$ in the subcritical regime and…

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…