The inverse problem for rough controlled differential equations

Ismaël Bailleul (1) , J. Diehl (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 FU Berlin - Institut für Mathematik

We provide a necessary and sufficient condition for a rough control driving a differentialequation to be reconstructable, to some order, from observing the resulting controlled evolution.Physical examples and applications in stochastic filtering and statistics demonstrate the practicalrelevance of our result.

Mots clés: signal reconstruction; rough differential equations; rough paths theory

Domaines: Probabilités [math.PR]

Ismaël Bailleul, J. Diehl. The inverse problem for rough controlled differential equations. SIAM Journal on Control and Optimization, 2015, 53 (5), pp.2762-2780. ⟨10.1137/140995982⟩. ⟨hal-01225321⟩