A functional approach to approximations for the observed open times in single ion channel models (Q1269660)

Consider an alternating renewal process with holding times \((X_n)_{n \in\mathbb{N}}\) in state 1 (open) and \((Y_n)_{n \in\mathbb{N}}\) in state 0 (closed), with distributions \(\mu_X\) and \(\mu_Y\), respectively. In practical applications of this stochastic model, in particular in connection with ion channels, sojourns in 0 of length less than some deadtime \(\tau\) are not observed, with the consequence that the distribution \(\nu\) of observed open times differs from \(\mu_X\). The paper develops approximation formulae for \(\nu= \Phi(\mu_X, \mu_Y,\tau)\) by a suitable expansion of \(\Phi\). Numerical examples show that these compare well to other approaches suggested previously.