Density Estimators of the Cumulative Reward up to a Hitting Time to a Rarely Visited Set of a Regenerative System

Marvin K Nakayama (1) , Bruno Tuffin (2)

1 NJIT - New Jersey Institute of Technology [Newark]
2 ERMINE - mEasuRing and ManagIng Network operation and Economic

For a regenerative process, we propose various estimators of the density function of the cumulative reward up to hitting a rarely visited set of states. The approaches exploit existing weak-convergence results for the hittingtime distribution, and we apply simulation (often with previously developed importance samplers for estimating the mean) to estimate parameters of the limiting distribution. We also combine these ideas with kernel methods. Numerical results from simulation experiments show the effectiveness of the estimators.

Domaines: Recherche opérationnelle [math.OC]

Marvin K Nakayama, Bruno Tuffin. Density Estimators of the Cumulative Reward up to a Hitting Time to a Rarely Visited Set of a Regenerative System. WSC 2022 - Winter Simulation Conference, Dec 2022, Singapour, Singapore. pp.1-18. ⟨hal-03709329⟩