Furthermore, they studied its asymptotic approximation ratio. Exponential stability is a form of asymptotic stability. Both the asymptotic and finite-sample behavior of most algorithms is well understood. This approach allows for more natural study of the asymptotic properties of the estimators. The above requires a definition of "asymptotic equivalence". Asymptotic analysis is used in several mathematical sciences. Asymptotic convergence results for contextual bandits were published in 2011. Hellinger distances are used in the theory of sequential and asymptotic statistics. This algorithm takes time (in asymptotic notation). The Bessel functions have the following asymptotic forms. In asymptotic theory, the standard approach is . It can be used to denote the asymptotic equality of two functions. Perhaps the most common distribution to arise as an asymptotic distribution is the normal distribution. These notations were used in applied mathematics during the 1950s for asymptotic analysis. Bernoulli numbers are also frequently used in other kinds of asymptotic expansions.