Area of Brownian Motion with Generatingfunctionology

Michel Nguyên Thê (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

This paper gives a survey of the limit distributions of the areas of different types of random walks, namely Dyck paths, bilateral Dyck paths, meanders, and Bernoulli random walks, using the technology of generating functions only.

Mots clés: Dyck path; Bernoulli random walk; Brownian motion; generating functions; weak convergence of stochastic processes.

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Géométrie algorithmique [cs.CG]

Michel Nguyên Thê. Area of Brownian Motion with Generatingfunctionology. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.229-242, ⟨10.46298/dmtcs.3321⟩. ⟨hal-01183916⟩