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arXiv · 2504.08864

Orthogonal series for si- and related processes, Karhunen-Lo\`eve decompositions

Kacha Dzhaparidze
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Abstract

This paper reproduces results from Chapter 11 of the forthcoming book \cite{dzh25}. It discusses series expansions of processes with stationary increments (si-processes) and certain associated processes. Making use of de Branges theory of Hilbert spaces of entire functions, it sheds new light on the existing literature and makes available some new results. In particular, it provides some new decompositions of the Karhunen-Lo\`eve type.

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Kacha Dzhaparidze. 2025-04-11. Orthogonal series for si- and related processes, Karhunen-Lo\`eve decompositions. https://arxiv.org/abs/2504.08864

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