Related papers: Penalty Method for Obliquely Reflected Diffusions
We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…
We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…
We present a method to estimate dense depth by optimizing a sparse set of points such that their diffusion into a depth map minimizes a multi-view reprojection error from RGB supervision. We optimize point positions, depths, and weights…
In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a…
The common and traditional method for dispersion compensation in optical domain is concatenating the transmit optical fiber by a compensating optical fiber having high-negative dispersion coefficient. In this paper, we take an opposite…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…
A general method for tight focusing of waves, based on compensation of the angular spectrum, is established. We apply the method to monochromatic, polychromatic and diffusive waves. Diffusive and monochromatic waves may form spatially…
The problem of calculation of the reflectivity of non-ideal shock-compressed plasmas is revisited. The dielectric formalism based on the method of moments incorporating exact asymptotic forms and sum rules is applied to the new experimental…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
A method for estimating the relative content of crystalline phases of a multiphase sample, based on probabilistic analysis of the intensities of the diffraction pattern reflexes, has been developed. The method is based on the introduction…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
A new $z$-stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing proper domain transformations, we solve corresponding…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…