In this paper, the strong limit theorems for arbitrary stochastic sequences are studied. Some convergence theorems for martingale difference sequence and a class of strong limit theorem for countable nonhomogeneous Markov chains are the particular cases of the results of this paper. Finally, the...

In this paper, we study the strong law of large numbers on the frequencies of states for a Markov chains field on a Bethe tree. In the proof, we apply a new technique in the study of the strong limit theorem.

Let {Xn, n[greater-or-equal, slanted]0} be a sequence of random variables on the probability space ([Omega],F,P) taking values in the alphabet S={1,2,...,N}, and Q be another probability measure on F, under which {Xn, n[greater-or-equal, slanted]0} is a Markov chain. Let h(P Q) be the sample...

In this paper, we study the strong law of large numbers and the Shannon–McMillan theorem for nonhomogeneous Markov chains indexed by a Cayley tree. This article generalizes the relative results of level nonhomogeneous Markov chains indexed by a Cayley tree.

In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete markets in terms of martingale deflators, present a recent...

We first study a local convergence theorem for countable Markov chains indexed by a homogeneous tree. As corollaries, we obtain some limit theorems for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by a homogeneous tree. Finally, we...

The expressions of solutions for general nxm matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke [Jaschke, S., 2003. A note on the inhomogeneous linear stochastic differential equation. Insurance: Mathematics and Finance 32,...

In this paper, we first study a convergence theorem for a finite mth-order nonhomogeneous Markov chain indexed by an m rooted Cayley tree. As corollaries, we obtain some limit theorems for the frequencies of occurrence of states for this Markov chain. Finally, we obtain the strong law of large...

This paper proposes some new classes of risk measures, which are not only comonotonic subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order. We give their representations in terms of Choquet integrals w.r.t. distorted probabilities, and show that if the...