Revisiting Stochastic Realization Theory using Functional Itô Calculus
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929244502753280 |
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| author | Veeravalli, Tanya Raginsky, Maxim |
| author_facet | Veeravalli, Tanya Raginsky, Maxim |
| contents | 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 Itô 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_10157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting Stochastic Realization Theory using Functional Itô Calculus Veeravalli, Tanya Raginsky, Maxim Optimization and Control Systems and Control Probability 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 Itô 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. |
| title | Revisiting Stochastic Realization Theory using Functional Itô Calculus |
| topic | Optimization and Control Systems and Control Probability |
| url | https://arxiv.org/abs/2402.10157 |