“…However, to the best of the authors' knowledge, most of the existing articles (see, e.g., [6,[12][13][14][15][16][17][18][19]) are only devoted to studying the local existence of mild solutions for stochastic evolution equations, and there are no results yet present on the existence of saturated mild solutions and global mild solutions for stochastic evolution equations in Hilbert spaces. Motivated by the abovementioned aspects, in this paper, by using Schauder's fixed point theorem, compact semigroup theory, and piecewise extension method, we investigate the existence of saturated mild solution and global mild solution for the initial value problem to a class of semilinear stochastic evolution equations in real separable Hilbert spaces.…”