Estimation in Discretely Observed Diffusions Killed at a Threshold

摘要: Parameter estimation in diffusion processes from discrete observations up to a first- passage time is clearly of practical relevance, but does not seem have been studied so far. In neuroscience, many models for the membrane potential evolution involve presence an upper threshold. Data are modelled as discretely observed diffusions which killed when threshold reached. Statistical inference often based on misspecified likelihood ignoring causing severe bias, e.g. bias incurred drift parameters Ornstein- Uhlenbeck model biological relevant can be 25-100 per cent. We compute or approximate function process. When estimating single trajectory, considerable may still present, and distribution estimates heavily skewed with huge variance. Parametric bootstrap effective correcting bias. Standard asymp- totic results do apply, consistency asymptotic normality recovered multiple trajectories observed, if mean first-passage through finite. Numerical examples illustrate experimental data set intracellular recordings mem- brane motoneuron analysed