In probability theory, the Lévy arcsine law, found by, states that the probability distribution of the time that Wiener process (which models Brownian motion) is positive is proportional to arcsin (√ "x").
In probability theory, the Lévy arcsine law, found by, states that the probability distribution of the proportion of the time that Wiener process (which models Brownian motion) is positive is a random variable whose probability distribution is the arcsine distribution. That distribution has a cumulative distribution function proportional to arcsin (√ "x").