Efficient Determination of a Finite Set of States for an Up-and-Down Process Possessing a Practical Closure

摘要

Conditions at which the up-and-down process with a step greater than 0.5 of the standard deviation of masking noise becomes practically closed on a finite set are investigated, e.g., the sufficient number of states of up-and-down process is determined so that the probability of obtaining other states is practically equal to zero. For this purpose, several lemmas on growth of the cumulative distribution function of standard normal distribution are proved. Formulas for a recursive calculation of the probability of obtaining the state of up-and-down process are obtained. Using them, an upper bound for obtaining other up-and-down process states is given.