NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes
We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$. These processes are central to continuous-time stochastic control, reinforcement learning, and mathematical finance. Although Wiener-chaos expansions offer strong theoretical tools, traditional computational methods are hindered by the need for large chaos dictionaries and high-order iterated integrals. To overcome these obstacles, we introduce NeuralChaos -- a neural operator architecture that produces elements of $\mathcal{H}^2_T(\mathbb{R}^{d})$ using only finitely many evaluations of the ...
| Authors | Anastasis Kratsios, Giulia Livieri, Philipp Schmocker |
|---|---|
| Primary category | math.PR |
| Published | 15 July 2026 |
| Last updated at source | 15 July 2026 |
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