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

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 $$1<q\le 2$$1<q≤2, allowing possibly infinite variance of the random entropy solutions of the scalar conservation law.