Related papers: L\'{e}vy Score Function and Score-Based Particle A…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…
This paper is concerned with nonparametric estimation of the L\'evy density of a pure jump L\'evy process. The sample path is observed at $n$ discrete instants with fixed sampling interval. We construct a collection of estimators obtained…
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…
Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
We obtain a simple direct derivation of the differential equation governing the entropy flow probability distribution function of a stochastic system first obtained by Lebowitz and Spohn. Its solution agrees well with the experimental…
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
In this paper we presented an overview on our works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's…
Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and…
We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by L\'{e}vy processes. Under some appropriate conditions, we show that the slow component of this…
The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and…
We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…