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In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections)…
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
In this paper is described the general aspect of a numerical method for piecewise determin-istic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov…
Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian…
A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter…
This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a…
We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer…
We present a computational alternative to probabilistic simulations for non-smooth stochastic dynamical systems that are prevalent in engineering mechanics. As examples, we target (1) stochastic elasto-plastic problems, which involve…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
We study the obtainment of closed-form formulas for the distribution of the jumps of a doubly-stochastic Poisson process. The problem is approached in two ways. On the one hand, we translate the problem to the computation of multiple…
In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic…
The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability $F(g)$ of a general time-inhomogeneous diffusion process to perturbations of the boundary $g$. We prove that, for boundaries $g\in C^2,$ this…
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
Working with systems of partial differential equations (PDEs) is a fundamental task in computational science. Well-posed systems are addressed by numerical solvers or neural operators, whereas systems described by data are often addressed…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…