Related papers: A backward Monte-Carlo method for time-dependent r…

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy…

We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…

Relativistic runaway electrons are a major concern in tokamaks. The European framework for Integrated Modelling (EU-IM), facilitates the integration of different plasma simulation tools by providing a standard data structure for…

Markov Chain Monte Carlo (MCMC) methods are algorithms for sampling probability distributions, commonly applied to the Boltzmann distribution in physical and chemical models such as protein folding and the Ising model. These methods enable…

Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…

Bayesian inversions followed by estimations of rare event probabilities are often needed to analyse groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution…

Two novel numerical estimators are proposed for solving forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. In contrast to the…

A complex notion of backward stochastic differential equation (BSDE) is proposed in this paper to give a probabilistic interpretation for linear first order complex partial differential equation (PDE). By the uniqueness and existence of…

In this work, we introduce a simple modification of the Monte Carlo algorithm, which we call step Monte Carlo (sMC). The sMC approach allows to simulate processes far from equilibrium and obtain information about the dynamic properties of…

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic…

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to…

Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…

This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…

Existence and local-uniqueness theorems for weak solutions of a system consisting of the drift-diffusion-Poisson equations and the Poisson-Boltzmann equation, all with stochastic coefficients, are presented. For the numerical approximation…

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…