Regularity characterization of asymptotically probability equivalent sequences

The notion of asymptotically equivalent sequences was presented by Pobyvanets in 1980. Using this definition, he presented Silverman–Toeplitz-type matrix conditions that ensure that a summability matrix preserves asymptotic equivalency. This work begins with an extension of Pobyvanets’ definition of convergence in probability. This definition is also used to present Silverman–Toeplitz-type conditions for ensuring that a summability matrix preserves asymptotic probability equivalence. In addition, we shall also present a Marouf-type characterization of such a sequence space.