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arXiv · 2607.22441

The martingale representation theorem for cylindrical martingale valued measures

S. Cambronero·D. Campos·C. A. Fonseca-Mora·D. Mena
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Abstract

We prove a martingale representation theorem for cylindrical martingale-valued measures defined on a separable Banach space. The main tool for establishing the theorem, is a new theory of non-radonifying stochastic integration in reflexive Banach spaces. A second one is the study and characterization of cylindrical white noise measure processes. As consequences of our representation theorem, we prove analogous versions for Hilbert space-valued measures and for cylindrical square integrable martingales. Finally, we apply the results to characterize the solutions to the weak martingale problem for SDEs driven by cylindrical white noise measures.

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S. Cambronero, D. Campos, C. A. Fonseca-Mora, D. Mena. 2026-07-24. The martingale representation theorem for cylindrical martingale valued measures. https://arxiv.org/abs/2607.22441

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