arXiv subjects

Elena Perfilev

Publications and source records attributed to Elena Perfilev.

3 recordsLinked to original sources

arXiv2019

Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion

This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptotics of the joint distribution of the length, maximum and the time at which this maximum is achieved. This result allows one to obtain a local central limit theorems for the length of the excursion conditioned on large values of the maximum.

math.PR↗

arXiv2019

Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments

We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.

math.PR↗

arXiv2017

Local asymptotics for the area under the random walk excursion

We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit theorem for the duration of the excursion conditioned on the large values of its area.

math.PR↗