An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems Articles uri icon

publication date

  • February 2016

start page

  • 577

end page

  • 597

issue

  • 2

volume

  • 66

International Standard Serial Number (ISSN)

  • 0885-7474

Electronic International Standard Serial Number (EISSN)

  • 1573-7691

abstract

  • The numerical approximation of boundary value problems by means of a probabilistic representations often has the drawback that the Monte Carlo estimate of the solution is substantially biased due to the presence of the domain boundary. We introduce a scheme, which we have called the leading-term Monte Carlo regression, which seeks to remove that bias by replacing a 'cloud' of Monte Carlo estimates—carried out at different discretization levels—for the usual single Monte Carlo estimate. The practical result of our scheme is an acceleration of the Monte Carlo method. Theoretical analysis of the proposed scheme, confirmed by numerical experiments, shows that the achieved speedup can be well over 100.

subjects

  • Mathematics

keywords

  • monte carlo method; romberg extrapolation; bounded difusión; feynman-kac formula; first exit time; parallel computing