The first passage time problem has attracted considerable research interest in the field of stochastic processes. It concerns the estimation of the probability density of the time for a random process to cross a specified boundary level. Even though there are many theoretical advances in solving this problem, for many classes of random processes no analytical solution exists. The jumpdiffusion ...

While kinetic Monte Carlo simulations can provide long-time simulations of the dynamics of physical and chemical systems, it is not yet possible in general to identify the inverse Monte Carlo attempt frequency with a physical timescale. Here we demonstrate such an identification by comparing simulations with experimental data. Using a dynamic lattice-gas model for the electrosorption of Br on A...

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those cha...

Many scientific and engineering applications involve the inversion of large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the Monte Carlo methods depend only on the number of chains and the length of those chains a...

Abstract. We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This resu...

Multi-level Monte Carlo is a relatively new method that computes expectations of stochastic processes to a desired tolerance significantly faster than previous methods. I will detail the basic idea of multi-level Monte Carlo and show how to implement it in the continuous time Markov chain setting, which is a modeling choice commonly used in the biosciences. Departments of Computer Science, Math...

In 2001 Heinrich, Novak, Wasilkowski and Woźniakowski proved that the inverse of the discrepancy depends linearly on the dimension, by showing that a Monte Carlo point set P of N points in the s-dimensional unit cube satisfies the discrepancy bound D∗s N (P)≤ cabssN with positive probability. Later their results were generalized by Dick to the case of double infinite random matrices. In the pre...

The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies. This large scale ill-posed inverse problem is explored by an intensive exploitation of an efficient 2D Maxwell solver, distributed on high performance compu...

Solving inverse problems in a complex, geologically realistic, and discrete model space and from a sparse set of observations is a very challenging task. Extensive exploration by Markov chain Monte Carlo (McMC) methods often results in considerable computational efforts. Most optimization methods, on the other hand, are limited to linear (continuous) model spaces and the minimization of an obje...