This paper studies the convergence rate of randomized quasi-Monte Carlo (RQMC) for discontinuous functions, which are often of infinite variation in the sense of Hardy and Krause.

Xiaoqun Wang, Ken Seng Tan, Pricing and Hedging with Discontinuous Functions: Quasi—Monte Carlo Methods and Dimension Reduction, Management Science, Vol. 59, No. 2 (February 2013), pp. 376-389 ...