A dichotomy for sampling barrier-crossing events of random walks with regularly varying tails
نویسندگان
چکیده
We consider the problem of sampling paths of a random walk up to the first time it crosses a fixed barrier, in the setting where the step sizes are iid with negative mean and have a regularly varying right tail. We study the efficiency of an AcceptanceRejection-type of simulation algorithm that is based on the change of measure proposed by Blanchet and Glynn [9]. We show that this algorithm is efficient if and only if the tail index α of the right tail lies in the interval (1, 3/2).
منابع مشابه
Ordered random walks with heavy tails ∗
This paper continues our previous work [4] where we have constructed a k-dimensional random walk conditioned to stay in the Weyl chamber of type A. The construction was done under the assumption that the original random walk has k− 1 moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index α < k−...
متن کاملState-independent Importance Sampling for Random Walks with Regularly Varying Increments
We develop state-independent importance sampling based efficient simulation techniques for two commonly encountered rare event probabilities associated with random walk (Sn : n ≥ 0) having i.i.d. regularly varying heavy-tailed increments; namely, the level crossing probabilities when the increments of Sn have a negative mean, and the the large deviation probabilities P{Sn > b}, as both n and b ...
متن کاملState-dependent Importance Sampling for Regularly Varying Random Walks
Consider a sequence (Xk : k ≥ 0) of regularly varying independent and identically distributed random variables with mean 0 and finite variance. We develop efficient rare-event simulation methodology associated with large deviation probabilities for the random walk (Sn : n ≥ 0). Our techniques are illustrated by examples, including large deviations for the empirical mean and path-dependent event...
متن کاملRandom sampling of long-memory stationary processes
This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the e...
متن کاملRare-event Simulation for Multidimensional Regularly Varying Random Walks
We consider the problem of e¢ cient estimation via simulation of rst passage time probabilities for a multidimensional random walk with regularly varying increments. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance in which the focus is a one dimensional random walk this problem captures important features of large deviations for multi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Applied Probability
دوره 54 شماره
صفحات -
تاریخ انتشار 2017