@inproceedings{08fd178b671f4bd1b368ff500ca458ea,

title = "Using regenerative simulation to calibrate exponential approximations to risk measures of hitting times to rarely visited sets",

abstract = "We develop simulation estimators of risk measures associated with the 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 the two risk measures of the hitting time. Numerical results demonstrate the effectiveness of our estimators.",

author = "Glynn, {Peter W.} and Nakayama, {Marvin K.} and Bruno Tuffin",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE; 2018 Winter Simulation Conference, WSC 2018 ; Conference date: 09-12-2018 Through 12-12-2018",

year = "2018",

month = jul,

day = "2",

doi = "10.1109/WSC.2018.8632477",

language = "English (US)",

series = "Proceedings - Winter Simulation Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1802--1813",

booktitle = "WSC 2018 - 2018 Winter Simulation Conference",

address = "United States",

}