Operator NJ-ODE achieves L^2-optimal prediction in infinite-dimensional spaces
New framework handles function-valued processes like yield curves without discretization loss.
The Operator Neural Jump ODE (NJ-ODE) framework, introduced by Florian Krach, Oliver Löthgren, and Josef Teichmann, tackles a long-standing limitation of stochastic process prediction: handling function-valued outputs without information loss. Traditional Neural Jump ODEs operate in finite-dimensional spaces, forcing function-valued problems such as yield curves or volatility surfaces to be discretized—a process that inherently discards detail. The new model instead lets the underlying process X take values directly in L^2(Ξ,ℝ^{d_X}), an infinite-dimensional function space, and produces a representative of the conditional expectation—the L^2-optimal predictor.
To prove convergence of the Operator NJ-ODE to the optimal prediction, the authors develop a novel approximation strategy that also generalizes previous finite-dimensional results under significantly weaker assumptions. This is crucial for real-world applications like online learning of continuous-time stochastic processes from discrete, irregular, and possibly incomplete observations. The work bridges neural operators with stochastic differential equations, opening the door to more accurate and granular predictions in finance, physics, and beyond—without the noise introduced by discretization.
- Extends Neural Jump ODEs to infinite-dimensional L^2 function spaces, avoiding discretization loss.
- Achieves L^2-optimal prediction by approximating the conditional expectation from irregular discrete data.
- New approximation strategy weakens assumptions and generalizes prior finite-dimensional convergence proofs.
Why It Matters
Enables precise, lossless predictions for financial yield curves and volatility surfaces from irregular real-world data.