Geometry of Stochastic Delay Differential Equations
نویسندگان
چکیده
منابع مشابه
Computational Method for Fractional-Order Stochastic Delay Differential Equations
Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...
متن کاملMixed Stochastic Delay Differential Equations
where W is a Wiener process, Z is a Hölder continuous process with Hölder exponent greater than 1/2, the coefficients a, b, c depend on the past of the process X . The integral with respect to W is understood in the usual Itô sense, while the one with respect to Z is understood in the pathwise sense. (A precise definition of all objects is given in Section 2.) We will call this equation a mixed...
متن کاملStochastic differential delay equations of population dynamics
In this paper we stochastically perturb the delay Lotka–Volterra model ẋ(t)= diag(x1(t), . . . , xn(t))[A(x(t)− x̄)+B(x(t − τ )− x̄)] into the stochastic delay differential equation (SDDE) dx(t)= diag(x1(t), . . . , xn(t)){[A(x(t)− x̄)+B(x(t − τ )− x̄)]dt + σ (x(t)− x̄)dw(t)}. The main aim is to reveal the effects of environmental noise on the delay Lotka–Volterra model. Our results can essentially ...
متن کاملAsymptotic 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...
متن کاملMultiscale Analysis of Stochastic Delay Differential Equations
We apply multi-scale analysis to stochastic delay-differential equations, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays of deterministic systems. Such models are particularly sensitive to noise when the system is near a critical point, which marks a transition to sustained oscillatory behavior in the deterministic system. In particula...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2005
ISSN: 1083-589X
DOI: 10.1214/ecp.v10-1151