Finitely additive and measurable stochastic games

Stochastic games with additive transitions

We deal with n-player AT stochastic games, where AT stands for additive transitions. These are stochastic games in which the transition probability vector ps(as), for action combination as 1⁄4 ðas ; . . . ; as Þ in state s, can be decomposed into player-dependent components as: 0377-2 doi:10. * Co E-m psðasÞ 1⁄4 Xn

Finitely Additive Equivalent

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L− L∞ ∩ L∞ = {0}, where the cl...

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenou...

On finitely additive vector measures.

In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.

Representing Finitely Additive Invariant Probabilities