An Unregularized Radial Kellerer Theorem

The paper proves an unregularized multidimensional Kellerer theorem for convex-order families of radially symmetric probability measures. Starting from Lowther’s canonical one-dimensional process, it constructs a continuous strong Markov martingale in Rd\mathbb{R}^dRd by assigning independent uniform directions to its radial excursions. A key contribution is the construction of canonical transition kernels that remain valid at stopping times.