Skip to Main content Skip to Navigation
Conference papers

Using Simulation to Calibrate Exponential Approximations to Tail-Distribution Measures of Hitting Times to Rarely Visited Sets

Abstract : We develop simulation estimators of measures associated with the tail distribution of the hitting time to a rarely visited set of states of a regenerative process. In various settings, the distribution of the hitting time divided by its expectation converges weakly to an exponential as the rare set becomes rarer. This motivates approximating the hitting-time distribution by an exponential whose mean is the expected hitting time. As the mean is unknown, we estimate it via simulation. We then obtain estimators of a quantile and conditional tail expectation of the hitting time by computing these values for the exponential approximation calibrated with the estimated mean. Similarly, the distribution of the sum of lengths of cycles before the one hitting the rare set is often well-approximated by an exponential, and we analogously exploit this to estimate tail measures of the hitting time. Numerical results demonstrate the effectiveness of our estimators.
Document type :
Conference papers
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01785210
Contributor : Bruno Tuffin <>
Submitted on : Friday, May 4, 2018 - 11:09:21 AM
Last modification on : Thursday, February 25, 2021 - 9:46:05 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 7:29:44 AM

File

wsc18-regenexp-HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01785210, version 1

Citation

Peter Glynn, Marvin Nakayama, Bruno Tuffin. Using Simulation to Calibrate Exponential Approximations to Tail-Distribution Measures of Hitting Times to Rarely Visited Sets. WSC 2018 - Winter Simulation Conference, Dec 2018, Gothenburg, Sweden. pp.1-11. ⟨hal-01785210⟩

Share

Metrics

Record views

666

Files downloads

94