Realization of Multi-Scale Stochastic Process on Multiple Tree

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This paper will describe a theoretical background and a possible application on the problem of realization of a certain class of stochastic multi-scale process. The realization problem of interest in this paper is to construct a multi-scale stochastic model to realize some pre-specified finest-scale covariance. Here, instead of focusing on a simple Haar system, a more general approach will be derived by introducing the so called Multiple Tree (MT). The main drawback in a plain Haar system, despite its successful applications, is the apparent blocky nature. This is due to a rather rough interpolator being used. It will be shown in this work that by a multiple tree it is possible to overcome such weakness. This characteristic will be apparent in the application part of this paper, in which a sample generation problem will be considered.

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