The Probability of Exceeding a High Boundary on a Random Time Interval for a Heavy-tailed Random Walk by Serguei Foss,1 Zbigniew Palmowski2 and Stan Zachary

نویسندگان

  • S. FOSS
  • Z. PALMOWSKI
چکیده

We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354–374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Probability of Exceeding a High Boundary on a Random Time Interval for a Heavy-tailed Random Walk

We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354–374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexam...

متن کامل

Asymptotics for the maximum of a modulated random walk with heavy-tailed increments

We consider asymptotics for the maximum of a modulated random walk whose increments ξXn n are heavy-tailed. Of particular interest is the case where the modulating process X is regenerative. Here we study also the maximum of the recursion given by W0 = 0 and, for n ≥ 1, Wn = max(0, Wn−1 + ξXn n ).

متن کامل

On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean and belonging, for some γ > 0, to a subclass of the class Sγ—see, for example, Chover, Ney, and Wainger (1973). For this subclass we give a probabilistic derivation of the asymptotic tail distribution of M , and show that extreme values of M are in general attained through some si...

متن کامل

On the asymptotics of the supremum of a random walk: the principle of a single big jump in the light-tailed case

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean and belonging, for some γ ≥ 0, to the class Sγ introduced by Chover, Ney, and Weinger (1973). For γ > 0, we give a probabilistic derivation of the asymptotic tail distribution of M and show that, as in the case γ = 0, extreme values of M are in general attained through some single...

متن کامل

On Exceedance Times for Some Processes with Dependent Increments

Let {Zn}n≥0 be a random walk with a negative drift and i.i.d. increments with heavy-tailed distribution and let M = supn≥0 Zn be its supremum. Asmussen & Klüppelberg (1996) considered the behavior of the random walk given that M > x, for x large, and obtained a limit theorem, as x→∞, for the distribution of the quadruple that includes the time τ = τ(x) to exceed level x, position Zτ at this tim...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005