Introduction: The mapping from neuronal activation to measured blood oxygenation level dependent (BOLD) signal in fMRI involves a complex interplay between physiological and physical processes that is yet to fully elucidated. Methods that account for the variability of the hemodynamic response function (HRF) have, with few exceptions (eg. and subsequent works), focused on parameterised, deterministic models of the HRF (eg. ). We propose a stochastic linear model (SLM) of the measured BOLD response, in which noise drives the neurovascular dynamics directly. The key difference between the SLM and the 'bilinear dynamical systems' approach  is that the SLM employs a fully stochastic model of the neurovascular response rather than attempting to separate stochastic neuronal activity from deterministic HRF's.