The Stochastic Coupling of SLE on the Strip Domain

The main work of this paper is to discuss the stochastic coupling of stirp SLEk (k ∈ (0,4]) on the stirp region Sπ. By constructing a bounded continuous local martingale, we prove that when a certain ordinary differential equation is satisfied, there is a coupling of two strip SLEk traces in Sπ;one is from a to b;the other is from b to a, such that the two curves visit the same set of points.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations （FBSDEs）. Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18： 143-177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.

A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations

In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.

Synchronization-Based Topology Identification of Uncertain Stochastic Delay Complex Networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

Near-Relaxed Control Problem of Fully Coupled Forward-Backward Doubly System

In this paper,we are concerned with an optimal control problem where the system is driven by a fully coupled forward-backward doubly stochastic differential equation.We study the relaxed model for which an optimal solution exists.This is an extension of initial control problem,where admissible controls are measure valued processes.We establish necessary as well as sufficient optimality conditions to the relaxed one.