Generating discrete-time constrained random walks and L\'evy flights

TL;DR

This paper presents an exact and efficient method for generating constrained discrete-time random walk trajectories, including bridges and other variants, with arbitrary jump distributions, useful for modeling complex stochastic processes.

Contribution

The authors develop a novel method to generate exact bridge trajectories for discrete-time random walks with arbitrary jumps, extending to generalized constrained walks.

Findings

Method efficiently generates bridge trajectories

Applicable to various jump distributions

Generalizes to other constrained walks like excursions and meanders

Abstract

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.