Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes

Matyas Barczy; Peter Kern

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arXiv · 1409.7253

Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes

Matyas Barczy·Peter Kern

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Abstract

We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge processes. As an application, we derive a formula for the density function of the supremum location of certain standardized Gauss-Markov processes on compact time intervals. We also present some sufficient conditions under which mean centered Gauss-Markov processes take zero at a fixed time with probability one.

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BibTeX RIS

Matyas Barczy, Peter Kern. 2014-09-25. Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes. https://arxiv.org/abs/1409.7253

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