Synchronization of discrete-time complex networks with randomly occurring coupling and distributed time-varying delay.
Synchronization of discrete-time stochastic neural networks with random delay.
The principle of the largest terms and quantum large deviations
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
The Uniqueness of the Transfer Function of Linear System from Input-Output Observations.
Théorie géométrique de la Représentation Markovienne
Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces
In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.
Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...
Weak solutions of stochastic differential inclusions and their compactness
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
Некоторые флуктуационные характеристики параметров возбудимости
Об усреднении недивергентных уравнений второго порядка со случайными коэффициентами