We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching SDDEsPJMSs . Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions a...

Abstract: The stability problem for a class of stochastic neural networks with Markovian jump parameters and leakage delay is addressed in this study. The sufficient condition to ensure an exponentially stable stochastic neural networks system is presented and proven with Lyapunov functional theory, stochastic stability technique and linear matrix inequality method. The effect of leakage delay ...

This paper considers the problem of computing an approximation system for a discrete-time Markovian jump system with mode-dependent time delays such that the H∞ norm of the error system is less than a prescribed scalar. It can be shown that the approximation system is constructed by the solutions of linear matrix inequalities (LMIs) with inverse constraints. An efficient algorithm is used to ob...

We propose a model for valuing participating life insurance products under a generalized jumpdiffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regimeswitching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experim...

This paper deals with a class of continuous-time uncertain singular linear systems with Markovian jump parameters and time delays. Sufficient conditions on stochastic stability and stochastic stabilizability are developed. A design algorithm for a state-feedback controller which guarantees that the closed-loop dynamic will be regular, impulse free and robustly stochastically stable is proposed ...

Abstract: This paper is considered with the problem of H∞ model reduction for a class of discrete-time 2D Markovian jump systems with state delays described by the Roesser model. Since these obtained conditions are not expressed as strict LMIs, the cone complementarily linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numeric...

In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the systems transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stab...

This paper considers the guaranteed cost control of singular Markovian jump systems (SMJSs) with time delay whose mode signal is inaccessible. The main contribution is to develop an approach to mode-independent guaranteed control, where the switching probability rate is also designed. New sufficient conditions of such controller are proposed in terms of linear matrix inequalities with some equa...

This paper presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLS). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to co...

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of processes, model not Markovian. In certain special circumstances, it Markovian generator if exciting function an exponential or sum fun...