5 research outputs found
Levy process simulation by stochastic step functions
We study a Monte Carlo algorithm for simulation of probability distributions
based on stochastic step functions, and compare to the traditional
Metropolis/Hastings method. Unlike the latter, the step function algorithm can
produce an uncorrelated Markov chain. We apply this method to the simulation of
Levy processes, for which simulation of uncorrelated jumps are essential.
We perform numerical tests consisting of simulation from probability
distributions, as well as simulation of Levy process paths. The Levy processes
include a jump-diffusion with a Gaussian Levy measure, as well as
jump-diffusion approximations of the infinite activity NIG and CGMY processes.
To increase efficiency of the step function method, and to decrease
correlations in the Metropolis/Hastings method, we introduce adaptive hybrid
algorithms which employ uncorrelated draws from an adaptive discrete
distribution defined on a space of subdivisions of the Levy measure space.
The nonzero correlations in Metropolis/Hastings simulations result in heavy
tails for the Levy process distribution at any fixed time. This problem is
eliminated in the step function approach. In each case of the Gaussian, NIG and
CGMY processes, we compare the distribution at t=1 with exact results and note
the superiority of the step function approach.Comment: 20 pages, 18 figure
Simplicial gauge theory and quantum gauge theory simulation
We propose a general formulation of simplicial lattice gauge theory inspired
by the finite element method. Numerical tests of convergence towards continuum
results are performed for several SU(2) gauge fields. Additionaly, we perform
simplicial Monte Carlo quantum gauge field simulations involving measurements
of the action as well as differently sized Wilson loops as functions of
.Comment: 20 pages, 6 figure
Simplicial gauge theory on spacetime
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime
simplicial meshes. The formulation is a generalization of classical lattice
gauge theory, and we prove consistency of the action in the sense of
approximation theory. In addition, we perform numerical tests of convergence
towards exact continuum results for several choices of gauge fields in pure
gauge theory.Comment: 18 pages, 2 figure
The Ekpyrotic Universe
The ekpyrotic universe is a brane cosmology theory with an alternative explanation of the big bang as a collision between two hyperplanes. We first introduce the reader to brane objects in the context of string theory, and then give an introduction to the standard hot big bang model and general properties of brane cosmology models. Thereafter follows a study of the ekpyrotic universe ending with a presentation and discussion of some new numerical results