P. Ackermann, G. Lorang, and B. Roynette, Independance of time and position for a random walk, Revista Matematica Iberoamericana, vol.20, issue.3, pp.915-917, 2004.

I. [. Gradstein and . Ryzhik, Table of integrals, series and products, 1980.

]. F. Kle05 and . Klebaner, Introduction to stochastic calculus with applications, 2005.

S. [. Karatzas and . Shreve, Brownian Motion and Stochastic Calculus
DOI : 10.1007/978-1-4684-0302-2

G. Lawler, Introduction to Stochastic Processes., Biometrics, vol.53, issue.2, 2006.
DOI : 10.2307/2533988

[. Norris, Markov chains, 1998.
DOI : 10.1017/CBO9780511810633

J. Pitman, One-dimensional brownian motion and the three-dimensional bessel process, Advances in Appl. Probabality, pp.511-526, 1975.

]. S. Res05 and . Resnick, Adventures in stochastic processes, 2005.

B. Roynette, P. Vallois, and M. Yor, Brownian penalisations related to excursion lengths, Article soumis aux Annales de l'Institut Henri Poincaré en octobre, 2006.
DOI : 10.1214/08-aihp177
URL : http://doi.org/10.1214/08-aihp177

M. [. Roynette and . Yor, Brownian penalisations, some exact results and metatheorems, p.133

. Mots-clés, Random walk ; Birth and death Markov processes ; penalization ; sojourn time ; Dynkin's formula ; random walk ; Brownian motion with drift ; Bessel chain and process ; change of probability