An Introduction to Probability Theory and Its Applications, Volume II

TL;DR: The evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size is considered, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w) which lead to an indefinite growth of the population fitness.

TL;DR: In this article, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of Open image in new window.

TL;DR: In this paper, the harmonic renewal function associated with C is the function G(x) = \sum\limits_1^\infty {n^{ - 1} } C(n)} (x), and the asymptotic behaviour of G to that of 1−C is linked.

TL;DR: In this article, the authors derived the asymptotic behavior of realized power variation of pure-jump Ito semimartingales as the sampling frequency within a fixed interval increases to infinity.