R. , D. Mauldin, M. Monticino, and . Heinrich-von-weizsäcker, Directionally reinforced random walks, Adv. Math, vol.117, issue.2, p.5, 1996.

S. Goldstein, On diffusion by discontinuous movements, and on the telegraph equation, Quart. J. Mech. Appl. Math, vol.4, issue.2, pp.129-156, 1951.

M. Kac, A stochastic model related to the telegrapher's equation, Papers arising from a Conference on Stochastic Differential Equations, vol.4, pp.497-509, 1972.

E. Renshaw and R. Henderson, The correlated random walk, J. Appl. Probab, vol.18, issue.2, pp.403-414, 1981.

G. H. Weiss, Aspects and applications of the random walk, Random Materials and Processes, 1994.

E. C. Eckstein, J. A. Goldstein, and M. Leggas, The mathematics of suspensions: Kac walks and asymptotic analyticity, Proceedings of the Fourth Mississippi State Conference on Difference Equations and Computational Simulations, vol.3, pp.39-50, 1999.

G. H. Weiss, Some applications of persistent random walks and the telegrapher's equation, Phys. A, vol.311, issue.3-4, pp.805-806, 2002.

J. Rissanen, A universal data compression system, IEEE Trans. Inform. Theory, vol.29, issue.5, pp.656-664, 1983.

P. Cénac, B. Chauvin, F. Paccaut, and N. Pouyanne, Context trees, variable length Markov chains and dynamical sources, Séminaire de Probabilités XLIV, vol.2046, pp.1-39, 2012.

I. Csiszár, Festschrift in honor of jorma rissanen on the occasion of his 75th birthday edited by peter grünwald, petri myllymäki, ioan tabus, marcelo weinberger, International Statistical Review, vol.76, issue.3, pp.436-437, 2008.

. 00062_1,

P. Cénac, B. Chauvin, S. Herrmann, and P. Vallois, Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes, Markov Process. Related Fields, vol.19, issue.1, p.10, 2013.

K. and B. Erickson, The strong law of large numbers when the mean is undefined, Trans. Amer. Math. Soc, vol.185, p.13, 1973.

P. Allaart and M. Monticino, Optimal stopping rules for directionally reinforced processes, Adv. in Appl. Probab, vol.33, issue.2, pp.483-504, 2001.

P. Allaart and M. Monticino, Optimal buy/sell rules for correlated random walks, J. Appl. Probab, vol.45, issue.1, pp.33-44, 2008.

D. Szász and B. Tóth, Persistent random walks in a one-dimensional random environment, J. Statist. Phys, vol.37, issue.1-2, pp.27-38, 1984.

B. Tóth, Persistent random walks in random environment, vol.71, pp.615-625, 1986.

R. Henderson, E. Renshaw, and D. Ford, A note on the recurrence of a correlated random walk, J. Appl. Probab, vol.20, issue.3, pp.696-699, 1983.

M. Lenci, Recurrence for persistent random walks in two dimensions, Stoch. Dyn, vol.7, issue.1, pp.53-74, 2007.

R. Siegmund, -. Schultze, and . Heinrich-von-weizsäcker, Level crossing probabilities. II. Polygonal recurrence of multidimensional random walks, Adv. Math, vol.208, issue.2, pp.680-698, 2007.

L. Horváth and Q. Shao, Limit distributions of directionally reinforced random walks, Adv. Math, vol.134, issue.2, pp.367-383, 1998.

R. Rastegar, Topics in self-interacting random walks. ProQuest LLC

P. Arka, R. Ghosh, A. Rastegar, and . Roitershtein, On a directionally reinforced random walk, Proc. Amer. Math. Soc, vol.142, issue.9, pp.3269-3283, 2014.

A. D. Kolesnik and E. Orsingher, A planar random motion with an infinite number of directions controlled by the damped wave equation, J. Appl. Probab, vol.42, issue.4, pp.1168-1182, 2005.

E. Orsingher and A. Gregorio, Random flights in higher spaces, J. Theoret. Probab, vol.20, issue.4, pp.769-806, 2007.

A. D. Kolesnik, Random motions at finite speed in higher dimensions, J. Stat. Phys, vol.131, issue.6, pp.1039-1065, 2008.

F. Comets, R. Fernández, and P. A. Ferrari, Processes with long memory: regenerative construction and perfect simulation, Ann. Appl. Probab, vol.12, issue.3, pp.921-943, 2002.

S. Gallo, Chains with unbounded variable length memory: perfect simulation and a visible regeneration scheme, Adv. in Appl. Probab, vol.43, issue.3, pp.735-759, 2011.

W. Feller, An introduction to probability theory and its applications, 1971.

, Hermann Thorisson. Coupling, stationarity, and regeneration. Probability and its Applications, 2000.

H. Kesten, The limit points of a normalized random walk, Ann. Math. Statist, vol.41, p.13, 1970.

M. Sholander, W. H. Harry-kesten, M. T. Ruckle, G. P. Boswell, R. Patil et al., Problems and Solutions: Advanced Problems: 5714-5719, Amer. Math. Monthly, vol.77, issue.2, pp.197-198, 1970.

H. Kesten, Problems and Solutions: Solutions of Advanced Problems: 5716, Amer. Math. Monthly, vol.78, issue.3, pp.305-308, 1971.

N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular variation, of Encyclopedia of Mathematics and its Applications, vol.27, p.12, 1989.

M. Mure?an, A concrete approach to classical analysis, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 2009.

C. Mortici, New forms of Stolz-Cesaró lemma, Internat. J. Math. Ed. Sci. Tech, vol.42, issue.5, pp.692-696, 2011.

K. B. Erickson and R. A. Maller, Drift to infinity and the strong law for subordinated random walks and Lévy processes, J. Theoret. Probab, vol.18, issue.2, pp.359-375, 2005.

S. R. Varadhan, Probability theory, Courant Lecture Notes in Mathematics, vol.7, 2001.

R. Durrett, Probability: theory and examples. Cambridge Series in Statistical and Probabilistic Mathematics, 2010.