Effect of randomly fluctuating environment on autotroph-herbivore model system.
Ergodicity and asymptotically almost periodic solutions of some differential equations.
Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form , . In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x|α, α ∈ [1/2,1). In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift
In this note we propose an exact simulation algorithm for the solution of (1)d X t = d W t + b̅ ( X t ) d t, X 0 = x, where b̅is a smooth real function except at point 0 where b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed equation (2)d X t β = d W t + b̅ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x towardsX solution of (1) as β ≠ 0 tends to 0. In this note, we show that this convergence...
Existence of -almost periodic solutions to a class of nonautonomous stochastic evolution equations.
Existence of solutions for second order stochastic differential inclusions in Hilbert spaces
In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
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