Integral Limit Theorems Taking Large Deviations into Account when Cramér’s Condition Does Not Hold. I

Nagaev, A. V.

doi:10.1137/1114006

Cited by 112 publications

(57 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the same asymptotics for τ x and ν x may be obtained for any distributions satisfying the asymptotic equivalence P{S n > na} ∼ nP{ξ 1 > na}. For instance, from the results of [20] it follows that such asymptotics hold for regularly varying distributions. The results of [27] imply that the same holds for Weibull-type distributions with a parameter smaller than 1/2.…”

Section: Heavy-tailed Distributions Imentioning

confidence: 63%

Asymptotics for the First Passage Times of Lévy Processes and Random Walks

Denisov

Shneer²

2013

J. Appl. Probab.

View full text Add to dashboard Cite

We study the exact asymptotics for the distribution of the first time τ x a Lévy process X t crosses a negative level −x. We prove that P(τ x > t) ∼ V (x)P(X t ≥ 0)/t as t → ∞ for a certain function V (x). Using known results for the large deviations of random walks we obtain asymptotics for P(τ x > t) explicitly in both light and heavy tailed cases. We also apply our results to find asymptotics for the distribution of the busy period in an M/G/1 queue.

show abstract

Section: Heavy-tailed Distributions Imentioning

confidence: 63%

Asymptotics for the First Passage Times of Lévy Processes and Random Walks

Denisov

Shneer²

2013

J. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…The case (W) with α < 1 and (I) are studied in [11,12] and [17], respectively, for the i.i.d. setting.…”

Section: Proofs Of Upper Boundsmentioning

confidence: 99%

Slowdown estimates for one-dimensional random walks in random environment with holding times

Dembo¹,

Fukushima²,

Kubota³

2018

Electron. Commun. Probab.

View full text Add to dashboard Cite

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We study the probability that the random walk travels slower than its typical speed and determine its decay rate asymptotic.2010 Mathematics Subject Classification. 60K37; 60F10; 60J75.

show abstract

“…In particular, this result implies that the standard Large Deviation Principle is not satisfied. For the asymptotic upper bound we have to appeal on the mathematical analysis originally started by Heyde [8,9] and Nagaev [10,11]. The q-exponential distribution belongs to the class of distributions they consider.…”

Section: Asymptotic Analysismentioning

confidence: 99%

“…Mathematicians have studied large deviations in the context of probability distributions with a fat tail starting with the works of Heyde [8,9] and Nagaev [10,11]. See also [12,13,14,15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%