N ov 2 00 6 Trees and asymptotic developments for fractional stochastic differential equations

Trees and asymptotic developments for fractional stochastic differential equations

In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/3. After solving this equation in a rather elementary way, following the approach of [10], we show how to obtain an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f : Rn → R is a regular function. With respect to [2], whe...

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...

On asymptotic stability of Weber fractional differential systems

In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.

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

2 6 N ov 2 00 4 The quantization complexity of diffusion processes by Steffen Dereich Technische

In this article, we study the high resolution quantization problem for Rdvalued stochastic processes X that are solutions of stochastic differential equations. We let C([0, 1],Rd) denote the set of continuous functions mapping [0, 1] to Rd and denote by ‖·‖[0,1] the corresponding supremum norm, i.e. ‖f‖[0,1] = supt∈[0,1] |f(t)|. Analogously, Lq([0, 1],Rd) denotes the Lq-space of functions mappi...