Protecting entanglement by detuning:in Markovian environments vs in non-Markovian environments

The models of two qubits separately trapped in two independent Markovian or non-Markovian environments have been investigated. The distinction of the two-qubit entanglement dynamics in different environments has also been discussed in detail. The results show that, in non-Markovian environments, the possible usage time of entanglement can be extended due to its memory effect. On the other hand, we note that, compared to Markovian environments, the two-qubit entanglement could be protected better in non-Markovian environments by modulating the detuning between qubits and cavities. Finally, an intuitive physicM interpretation for these results is given.

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

A Markov decision problem in a risk model with interest rate and Markovian environment

We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued premium per unit time, and introducing a control strategy of periodic dividend payments. A Markov decision problem arises and the control objective is to maximize the cumulative expected discounted dividends paid to the shareholders until ruin minus a discounted penalty for ruin. We show that under the absence of a ceiling of dividend rates the optimal strategy is a conditional band strategy given the current state of the environment process. Under the presence of a ceiling for dividend rates, the character of the optimal control strategy is given. In addition, we offer an algorithm for the optimal strategy and the optimal value function.Numerical results are provided to illustrate the algorithm and the impact of the penalty.

A Periodic Dividend Problem with Inconstant Barrier in Markovian Environment

Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.