Open AccessPosted Content
The maximum on a random time interval of a random walk with long-tailed increments and negative drift
Serguei Foss,Stan Zachary +1 more
Reads0
Chats0
TLDR
In this article, the authors studied the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift, and extended to a general stopping time.Abstract:
We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen (1998), simplify its proof, and give some converses.read more
Citations
More filters
Book
An Introduction to Heavy-Tailed and Subexponential Distributions
TL;DR: In this article, heavy and long-tailed distributions were used for both local and global random walk distributions, and local probabilities for each random walk were derived. But the results were not generalized to include local probability distributions.
Journal ArticleDOI
Convolution equivalence and infinite divisibility
TL;DR: In this paper, the tail behavior of a compound Poisson distribution function is related to that of its Levy measure when one of them is convolution equivalent, and a tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
Journal ArticleDOI
Asymptotics for sums of random variables with local subexponential behaviour
TL;DR: In this paper, the authors studied distributions F on [0, infinity] such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, X + T).
Journal ArticleDOI
Asymptotics of randomly stopped sums in the presence of heavy tails
TL;DR: In this paper, the authors studied conditions under which P{S� > x} ∼ P{M� > X} ∼ EP{�1 > x] as x → ∞, where Sis a sum �1 +... + �� of random size and Mis a maximum of partial sums M� = maxn�� Sn.
Journal ArticleDOI
State-dependent importance sampling for rare-event simulation: An overview and recent advances
Jose Blanchet,Henry Lam +1 more
TL;DR: This paper surveys recent techniques that have been developed for rare-event analysis of stochastic systems via simulation, and reviews standard (state-independent) techniques that take advantage of large deviations results for the design of efficient importance sampling estimators.
References
More filters
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Journal ArticleDOI
Estimates for the probability of ruin with special emphasis on the possibility of large claims
Paul Embrechts,Noel Veraverbeke +1 more
TL;DR: In this article, the authors investigated the asymptotic behavior of the probability of ruin function when the initial risk reserve tends to infinity and gave a thorough treatment of the latter and also reviewed previously known but mostly scattered results.
Related Papers (5)
Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments
On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions
Stan Zachary,Sergey Foss +1 more