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math.NA2026
Extended Walk-on-Spheres Algorithm for Linear and Nonlinear Elliptic Problems of Divergence-type
Iulian Cîmpean, Andreea Grecu, Arghir Zarnescu
The Walk-on-Spheres algorithm, introduced by M. E. Muller in 1956, is a well known Monte Carlo method that leverages Brownian exit distributions from spheres to solve the Laplace e…
math.PR2026
Regularization of the superposition principle: Potential theory meets Fokker-Planck equations
Lucian Beznea, Iulian Cîmpean, Michael Röckner
For a solution to a (possibly nonlinear) Fokker-Planck equation (FPE) the powerful superposition principle renders a probability measure on path space with one dimensional time mar…