A converse to Pitman's theorem for a space-time Brownian motion in an affine Weyl chamber

Manon Defosseux (1) , Charlie Herent (2, 1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

We prove an inverse Pitman's theorem for a space-time Brownian motion conditioned in Doob's sense to remain in an affine Weyl chamber. Our theorem provides a way to recover an unconditioned space-time Brownian motion from a conditioned one applying a sequence of path transformations.

Domains: Probability [math.PR]

Manon Defosseux, Charlie Herent. A converse to Pitman's theorem for a space-time Brownian motion in an affine Weyl chamber. 2024. ⟨hal-03840191v3⟩