Revisiting Stochastic Realization Theory using Functional It\^o Calculus

Tanya Veeravalli; Maxim Raginsky

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arXiv · 2402.10157

Revisiting Stochastic Realization Theory using Functional It\^o Calculus

Tanya Veeravalli·Maxim Raginsky

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Abstract

This paper considers the problem of constructing finite-dimensional state space realizations for stochastic processes that can be represented as the outputs of a certain type of a causal system driven by a continuous semimartingale input process. The main assumption is that the output process is infinitely differentiable, where the notion of differentiability comes from the functional It\^o calculus introduced by Dupire as a causal (nonanticipative) counterpart to Malliavin's stochastic calculus of variations. The proposed approach builds on the ideas of Hijab, who had considered the case of processes driven by a Brownian motion, and makes contact with the realization theory of deterministic systems based on formal power series and Chen-Fliess functional expansions.

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BibTeX RIS

Tanya Veeravalli, Maxim Raginsky. 2024-02-15. Revisiting Stochastic Realization Theory using Functional It\^o Calculus. https://arxiv.org/abs/2402.10157

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