Revisiting Stochastic Realization Theory using Functional It\^o Calculus
<|reference_start|>Revisiting Stochastic Realization Theory using Functional It\^o Calculus: 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.<|reference_end|>
@article{veeravalli2024revisiting,
    title={Revisiting Stochastic Realization Theory using Functional It\^o Calculus},
    author={Tanya Veeravalli and Maxim Raginsky},
    journal={arXiv preprint arXiv:2402.10157},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10157},
    primaryClass={math.OC cs.SY eess.SY math.PR}
}