Correction to: Multilevel Monte Carlo front-tracking for random scalar conservation laws

Abstract

An error in [4, Theorem 4.1, 4.5, Corollary 4.5] is corrected. There, in the Monte Carlo error bounds for front tracking for scalar conservation laws with random input data, 2-integrability in a Banach space of type 1 was assumed. In providing the corrected convergence rate bounds and error versus work analysis of multilevel Monte Carlo front-tracking methods, we also generalize [4] to q-integrability of the random entropy solution for some 1 < q ≤ 2, allowing possibly infinite variance of the random entropy solutions of the scalar conservation law.

Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux

“…Note that restricting ourselves to a bounded domain will enable us to prove error estimates of the Monte Carlo and multilevel Monte Carlo finite volume method also in L 2 (Ω; L 1 (D)) (cf. [44]).…”