Long runs under point conditioning. The real case.

Michel Broniatowski (1) , Virgile Caron (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to innity. The conditioning event is of moderate or large deviation type. The result extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An algorithm for the simulation of such long runs is presented, together with an algorithm determining their maximal length for which the approximation is valid up to a prescribed accuracy.

Mots clés: Gibbs principle; conditioned random walk; large deviation; moderate deviation; simulation

Domaines: Applications [stat.AP]

Michel Broniatowski, Virgile Caron. Long runs under point conditioning. The real case.. 2010. ⟨hal-00517338⟩