A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Chapter 8. Applications to the Random Walk on Spheres method
[chapter]

1997
*
Spherical Means for PDEs
*

The integral equations with a convergent Neumann series can be numerically solved by the Monte Carlo method using the Markov chains [10]. To make things clear we first illustrate the situation by a simple evaluation of the spherical mean (in R 3 ) by the Monte Carlo method. Let s be a random vector uniformly distributed on the sphere 5(x, r). Then by definition, the expectation of the random variable u(s) is equal to the spherical mean Nru: Eu(s) = Nru = J-j J u(y) dS(y) . (8.1) S(*,r) By the

doi:10.1515/9783110926026-009
fatcat:ujpdzzthprb2bmrpgo4lfacqha