Existence of square-mean almost periodic mild solutions to some nonautonomous stochastic second-order differential equations.
Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation.
Explosion time in stochastic differential equations with small diffusion.
Exponential stability for a class of singularly perturbed Itô differential equations.
Exponential stability of stochastic discrete-time, periodic systems in Hilbert spaces.
Exponentially discounted estimates and oscillations in linear controlled systems
Filippov approach in stochastic maximum principle without differentiability assumptions.
Finite-time synchronization of chaotic systems with noise perturbation
In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical...
First-order autoregressive processes with time-dependent random parameters
Functional integro-differential stochastic evolution equations in Hilbert space.
General theorems for numerical approximation of stochastic processes on the Hilbert space .
Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.
Introducing randomness into first-order and second-order deterministic differential equations.
Invariant measures related with randomly connected Poisson driven differential equations
We consider the stochastic differential equation (1) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup describing the evolution of measures along trajectories and vice versa.
Kermack-McKendrick epidemic model revisited
This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size . Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer...
Liens entre équations différentielles stochastiques et ordinaires
Linear boundary value problem in Banach space with random element in two-point boundary condition
Linear random boundary value problems containing weakly correlated forcing functions.
Measure-differential inclusions in percussional dynamics.
Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations
For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility...