1 research outputs found
Monte Carlo solution for the Poisson equation on the base of spherical processes with shifted centres
We consider a class of spherical processes rapidly
converging to the boundary (so called Decentred
Random Walks on Spheres or spherical processes
with shifted centres) in comparison with the
standard walk on spheres. The aim is to compare
costs of the corresponding Monte Carlo estimates
for the Poisson equation. Generally, these costs
depend on the cost of simulation of one trajectory
and on the variance of the estimate.
It can be proved that for the Laplace equation the
limit variance of the estimation doesn\u27t depend on
the kind of spherical processes. Thus we have very
effective estimator based on the decentred random
walk on spheres. As for the Poisson equation, it
can be shown that the variance is bounded by a
constant independent of the kind of spherical
processes (in standard form or with shifted
centres). We use simulation for a simple model
example to investigate variance behavior in more
details