Related papers: Efficient estimation of one-dimensional diffusion …
In [4], it is proved that we can have a continuous first-passage-time density function of one dimensional standard Brownian motion when the boundary is H\"older continuous with exponent greater than 1/2. For the purpose of extending [4]…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of…
An exact Quantum Kinetic Monte Carlo method is proposed to calculate electron transport for 1D Fermi Hubbard model. The method is directly formulated in real time and can be applied to extract time dependent dynamics of general interacting…
In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…
We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a $2D$ domain. For this system, the coupling of translational and rotational diffusion makes the process ${\bf x} (t)$ of the positions of the…
A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…
There are known expressions to calculate the moments of the first passage time in Markov chains. Nevertheless, it is commonly forgotten that in most applications the parameters of the Markov chain are constructed using estimates based upon…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
We study, through the diffusion Monte Carlo method, a spin one-half fermion fluid, in the three dimensional Euclidean space, at zero temperature. The point particles, immersed in a uniform "neutralizing" background, interact with a…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We develop a model to compute the first-passage time of a random walker in a crowded environment. Hard-core particles with the same size and diffusion coefficient than the tracer diffuse, and the model allows to compute the first passage…
The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range…
We describe two distinct approaches to obtaining cloud point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand canonical ensemble. The first method determines the chemical…