Monte Carlo method and the random isentropic Euler system
Abstract
Abstract We show several results on the convergence of the Monte Carlo method applied to a family of consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our approach is based on a combination of several new ideas developed recently in the context of the Euler system: The concept of a dissipative weak solution as a universal closure of families of consistent approximations. A set–valued version of the Strong law of large numbers for general multivalued mappings with closed range. Application of the Komlós version of the convergence of empirical averages of integrable functions. Unconditionally convergent finite volume approximation schemes. The theoretical results are illustrated by a series of numerical simulations obtained by a viscosity finite volume scheme combined with the Monte Carlo method.
Fields of Study & Subjects
Stochastic processes and financial applications
Mathematical Approximation and Integration
Mathematical functions and polynomials
Publication details
- Journal / source
- Stochastic Partial Differential Equations Analysis and Computations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 14
- Issue
- 4
- Pages
- 2247-2278
- Publication date
- 7 April 2026
- Language
- EN