High-resolution quantization and entropy coding for fractional Brownian motion

2 3 A pr 2 00 5 High - resolution quantization and entropy coding for fractional Brownian motion

We derive a high-resolution formula for the quantization and entropy coding approximation quantities for fractional Brownian motion, respective to the supre-mum norm and L p [0, 1]-norm distortions. We show that all moments in the quanti-zation problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremu...

High-resolution product quantization for Gaussian processes under sup-norm distortion

We derive high-resolution upper bounds for optimal product quantization of pathwise contionuous Gaussian processes respective to the supremum norm on [0, T ]. Moreover, we describe a product quantization design which attains this bound. This is achieved under very general assumptions on random series expansions of the process. It turns out that product quantization is asymptotically only slight...

High resolution coding of stochastic processes and small ball probabilities

In this thesis, we study the high resolution coding problem for stochastic processes. The general coding problem concerns the finding of a good representation of a random signal, the original, within a class of allowed representations. The class of allowed representations is defined through restrictions on the information content of these representations. Mostly we consider three different inte...

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

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory