Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"><mml:mi>G</mml:mi></mml:math>-Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Parametric Estimation for Linear Stochastic Delay Differential Equations Driven by Fractional Brownian Motion

Consider a linear stochastic differential equation dX(t) = (aX(t) + bX(t− 1))dt+ dW t , t ≥ 0 with time delay driven by a fractional Brownian motion {WH t , t ≥ 0}. We investigate the asymptotic properties of the maximum likelihood estimator of the parameter θ = (a, b).

On delay-dependent stability for a class of nonlinear stochastic delay-differential equations

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of ...

Asymptotic Behaviours of Stochastic Differential Delay Equations

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asympt...

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion