Related papers: From the Stochastic Embedding Sufficiency Theorem …
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…
We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…
Scattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
We develop a convergence theory for non-monotone approximation schemes for fully nonlinear parabolic partial differential equations. Modern computational methods such as kernel-based collocation, spectral methods, physics-informed neural…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…
We discuss the effective diffusion constant $D_{{\it eff}}$ for stochastic processes with spatially-dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived…
In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed supersymetric theory of stochastic differential equations (SDE). It turns out that the stochastically…