Monte Carlo estimation of the solution of fractional partial differential equations

Vassili Kolokoltsov, Feng Lin, Aleksandar Mijatović

Research output: Contribution to journalArticlepeer-review

Abstract

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of errors between the exact solution and the Monte Carlo approximation, the estimate of the fluctuation via the appropriate central limit theorem (CLT) and the construction of confidence intervals. Moreover, we provide rates of convergence in the CLT via Berry-Esseen type bounds. Concrete numerical computations and illustrations are included.

Original languageEnglish
Pages (from-to)278-306
Number of pages29
JournalFractional Calculus and Applied Analysis
Volume24
Issue number1
DOIs
StatePublished - 1 Feb 2021

Scopus subject areas

  • Analysis
  • Applied Mathematics

Keywords

  • Berry-Esseen bounds
  • Central limit theorem
  • Monte-Carlo estimation
  • Numerical solution of fractional PDE
  • Simulation
  • Stable process

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