相关论文: Non-reversible lifts of reversible diffusion proce…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…

The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…

A kinetics built upon $q$-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the "quasi-position" whose eigenvalues are the levels of…

Inference-time algorithms are an emerging paradigm in which pre-trained models are used as subroutines to solve downstream tasks. Such algorithms have been proposed for tasks ranging from inverse problems and guided image generation to…

A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…

We consider continuous--time Markov kinetics with a finite number of states and a given positive equilibrium distribution P*. For an arbitrary probability distribution $P$ we study the possible right hand sides, dP/dt, of the Kolmogorov…

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…

This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and…

We prove convergence of symmetric diffusions on Wiener spaces by using stopping times arguments and capacity techniques. The drifts of the diffusions can be singular, we require the densities of the processes to be neither bounded from…

In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic…

In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a…

A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited assumptions about the transport field, which might be…

Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…

The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…

In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates,…

We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally…