Generating discrete-time constrained random walks and Lévy flights – Archive ouverte HAL

Benjamin de Bruyne ¹ Satya N. Majumdar ¹ Grégory Schehr ² Satya Majumdar ¹

Benjamin de Bruyne, Satya N. Majumdar, Grégory Schehr, Satya Majumdar. Generating discrete-time constrained random walks and Lévy flights. Physical Review E , American Physical Society (APS), 2021, 104 (2), ⟨10.1103/PhysRevE.104.024117⟩. ⟨hal-03388308⟩

We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly accounts for the bridge constraint. It is illustrated on various jump distributions and is shown to be very efficient in practice. In addition, we show how to generalize the method to other types of constrained random walks such as generalized bridges, excursions, and meanders.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTHE – Laboratoire de Physique Théorique et Hautes Energies