Related papers: Pathwise differentiability of reflected diffusions…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…
Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic PDE from measurements. The convex energy functional method with Tikhonov regularization is applied to tackle this problem. For the discretization…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a…
The atmospheres of (exo) planets and moons, as well as reflection nebulae, contain in general independently scattering particles in random orientation and are often supposed to be plane-parallel. Relations are presented for the…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations,…
We consider stochastic differential equations with (oblique) reflection in a $2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood of the origin has the form $\{(x_1,x_2):0<x_1\leq\delta_0,\psi_1(x_1)<x_2<\psi_…
Diffusion processes $(\underline{\bf X}_d(t))_{t\geq 0}$ moving inside spheres $S_R^d \subset\mathbb{R}^d$ and reflecting orthogonally on their surfaces $\partial S_R^d$ are considered. The stochastic differential equations governing the…
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation…
We investigate diffusion-type partial differential equations that are irregular in the sense that they admit weak solutions which are nowhere smooth, even for prescribed smooth data. By reformulating these equations as first-order partial…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential…
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…