A probabilistic representation of constants in Kesten’s renewal theorem

Mazur-Ulam theorem in probabilistic normed groups

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

A Probabilistic Kleene Theorem

We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equ...

1 Existence of Limit Constants in Probabilistic

Hyperseparoids: A Representation Theorem

In this note, hyperseparoids are introduced; hyperseparoids are to separoids as Tverberg’s theorem is to Radon’s theorem. Also, a geometric representation theorem for acyclic kseparoids is presented which generalises that for separoids exhibited in [2].

Convergence rates in the local renewal theorem

We study subgeometric convergence rates in the local renewal theorem, which plays an important role in obtaining results on convergence rates for Markov chains [4]. Let {ξn}n≥0 and {ξ ′ n}n≥0 be two sequences of mutually independent and integervalued r.v.’s. Assume further that (i) ξ0 and ξ ′ 0 are non-negative r.v.’s; (ii) all {ξn}n≥1 and {ξ ′ n}n≥1 are i.i.d. and strictly positive, with a com...