Some issues in multivariate stochastic root finding

The stochastic root finding problem (SRFP) involves finding points in a region where a function attains a prespecified target value, using only a consistent estimator of the function. Due to the properties that the SRFP contexts entail, the development of good solutions to SRFPs has proven difficult, at least in the multi-dimensional setting. This paper discusses certain key issues, insights and complexities for SRFPs. Some of these are important in that they point to phenomena that contribute to the difficulties that arise in the development of efficient algorithms for SRFPs. Others are simply observations, sometimes obvious, but important for providing useful insight into algorithm development.