相关论文: Quantitative diffusion approximation for the Neutr…

By using the spectrum of the underlying symmetric diffusion operator, the convergence in $L^p$-Wasserstein distance $\mathbb W_p (p\ge 1)$ is characterized for the empirical measure $\mu_t$ of non-symmetric subordinated diffusion processes…

We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a…

In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…

We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…

The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…

We study the weak approximation error of a skew diffusion with bounded measurable drift and H\"older diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first…

We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional…

The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…

For a Markov process associated with a diffusion type Dirichlet form an upper bound is shown for the law of the finite dimensional distributions of the process. Under some more assumptions on the underlaying space this is also shown for the…

Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…

For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the…

RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a…

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…

We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function…

The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…

Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…