Stationary Transformation of Integrated Brownian Motion

Details Stationary Transformation of Integrated Brownian Motion Stationary Transformation of Integrated Brownian Motion

2004-12-15

arxiv.org/abs/math/0412291v1

Mathematics

Probability

18 pages

Scientific paper

Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family of processes, but their spectral representation is also useful in dealing with integrated Brownian motion. We illustrate this by deriving an explicit representation for the joint density function for a family of integrated Brownian motions and showing some of its properties.

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