Related papers: Diffusion processes with weak constraint through p…

We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…

We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of…

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic…

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…

Denoising diffusions sample from a probability distribution $\mu$ in $\mathbb{R}^d$ by constructing a stochastic process $({\hat{\boldsymbol x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that ${\hat{\boldsymbol x}}_0$ is easy to sample, but the…

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…

For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of the density from which we derive some explicit Gaussian…

In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…

This paper studies the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the…

Diffusion models have been successfully adapted to text generation tasks by mapping the discrete text into the continuous space. However, there exist nonnegligible gaps between training and inference, owing to the absence of the forward…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…

For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…

Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…

Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump-diffusion on…

We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…