Paper / 2026
Strong Measurability and Adapted Approximations with Applications to Non-Markovian Control
Measurability and adapted approximation tools for metric-space-valued maps, with applications to path-dependent stochastic control.
- Authors
- Keivan Mirzaei, Jinniao Qiu
- Institution
- University of Calgary
- Status
- Preprint
Overview
When a stochastic control problem depends on past observations, approximating the model must preserve both its history dependence and the information available to each decision. This paper develops tools for measurable maps with possibly nonseparable metric-space targets and for adapted stochastic processes.
Contributions
- Criteria for strong measurability, including results under the continuum hypothesis and separate conditions on the density of the target space.
- Approximations of adapted processes and Lipschitz functionals involving paths and probability laws, including smooth approximations based on finitely many observations.
- Applications to controlled stochastic differential equations in separable Hilbert spaces: under the continuum hypothesis and the paper’s assumptions, states and costs converge uniformly over admissible controls, optimal values converge, and near-optimal controls can be transferred.
Preprint
First submitted to arXiv on September 23, 2026.