1 Interacting Particle Systems for the Computation of Rare Events 2 1.1 Twisted Feynman-Kac Expectations . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 IPS and Empirical Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Model Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Convergence Results . . . . . . . . . . . . . . . . . . . . . . ....

We present a second heuristic FKN formula for fermions which is more suitable for constructing relativistic fields in the interacting case than our first attempt. The FKN formula remains Hermitean, and the Euclidean Dirac fields remain undoubled. This version is based on a local extension of Osterwalder-Schrader positivity to overlapping, Euclidean time arguments, which is not quite so immediat...

In this paper, we study the propagation speeds of reaction-diffusion-advection (RDA) fronts in time-periodic cellular and chaotic flows with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We first apply variational principle to reduce computation KPP front a principal eigenvalue problem linear advection-diffusion operator space-time periodic coefficients on domain. To end, develop efficient ...

In this dissertation, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in 3d and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann and Robin boundary conditions respectively. Approximations of RBM based on a walk-on-spheres (WOS) and random walk on lattices are discussed and tested for sampl...