Generating discrete-time constrained random walks and Lévy flights
Benjamin De Bruyne, Satya N. Majumdar, Grégory Schehr
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.
Topics & Concepts
JumpRandom walkLévy flightConstraint (computer-aided design)Statistical physicsMathematicsDistribution (mathematics)Bridge (graph theory)Discrete time and continuous timeApplied mathematicsMathematical analysisPhysicsGeometryStatisticsMedicineInternal medicineQuantum mechanicsDiffusion and Search DynamicsFractional Differential Equations SolutionsStochastic processes and statistical mechanics