77 citations · 471 across the 42 of their papers we have counts for
45 papers
Does 2026 AI exhibit intelligence, or can Claude outsmart Pierre or Catherine ?
Robert C. Dalang
Using a sequence of high-school level mathematics questions that were not available on the Internet, we compare the performance of the popular AI software Claude with that of my fr…
A simple derivation of the Fourier transform of the Heaviside function
Robert C. Dalang
We give a rigorous derivation of the Fourier transform of the Heaviside function within a framework for tempered distributions that is suitable for undergraduate engineering and ma…
Asymptotic behavior of the stochastic heat equation over large intervals
David Candil, Robert C. Dalang, Marta Sanz Solé
We consider a nonlinear stochastic heat equation on , driven by a space-time white noise , with a given initial condition an…
Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
Robert C. Dalang, David Nualart, Fei Pu
For Gaussian random fields with values in , sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in…
Sample path properties of parabolic SPDEs with non constant coefficients
Robert C. Dalang, Marta Sanz-Solé
We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and…
Stochastic Control Problems Motivated by Sailboat Trajectory Optimization
Carlo Ciccarella, Robert C. Dalang, Laura Vinckenbosch
We develop a mathematical model for sailboat navigation that captures the essential features of the problem and can provide insights that might not be available otherwise. In our m…