Computing the principal eigenelements of some linear operators using a branching Monte Carlo method

In earlier work, we developed a Monte Carlo method to compute the principal eigenvalue of linear operators, which was based on the simulation of exit times. In this paper, we generalize this approach by showing how to use a branching method to improve the efficacy of simulating large exit times for the purpose of computing eigenvalues. Furthermore, we show that this new method provides a natural estimation of the first eigenfunction of the adjoint operator. Numerical examples of this method are given for the Laplace operator and an homogeneous neutron transport operator.