IJPAM: Volume 101, No. 2 (2015)

TAIL BEHAVIOR OF THE SUPREMUM OF A RANDOM
WALK WITH HEAVY-TAILED INCREMENTS
AND PERTURBATIONS

Changjun Yu$^1$, Dongya Cheng$^2$
$^1$School of Sciences
Nantong University
Nantong, 226019, P.R. CHINA
$^2$School of Mathematical Sciences
Soochow University
Suzhou, 215006, P.R. CHINA


Abstract. Let $\{\xi_n, n\geq 1\}$ be a sequence of independent and identically distributed random variables with a common distribution $F$ and $\{\eta_n, n\geq 1\}$ a sequence of independent normal random variables with zero means and different variances. Set $T_n=\sum\limits_{i=1}^nX_i, n\geq1$ and $T_0=0$, where $X_i=\xi_i+\eta_i, 1\le i\leq n$. Under conditions that the two sequences of random variables are independent to each other and the integrated tail distribution of $F$ belongs to the subexponential distribution class, we derive the asymptotic tail behavior of the supremum of the partial sums $T_n, n\geq0$.

Received: October 28, 2014

AMS Subject Classification: 60F15

Key Words and Phrases: random walks, subexponential distributions, asymptotic behavior

Download paper from here.




DOI: 10.12732/ijpam.v101i2.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 2
Pages: 223 - 232


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).