M. Alcalde Navarro, G. Sanz Sáiz, M. Lafuente Blasco

Let $\delta$ be a real number and $\{X_j\}_{j\ge 1}$ be a sequence of random variables. An observation $X_n$ is said to be a $\delta$-record if
X_n>\max\{X_1,\ldots,X_{n-1}\} + \delta.
This generalization of the concept of record observation is especially interesting when $\delta <0$ as $\delta$-records show up more frequently. We analyze the well-known Linear Drift Model (LDM) $Y_n = X_n + cn$, $n\ge 1$, assuming that the residuals $\{X_n\}_{n\ge 1}$ are strongly stationary and strong mixing. Our purpose is to study the asymptotic behaviour of the sample $\delta$-record rate $N_{n,\delta}/n$. A Central Limit Theorem and a Law of Iterated Logarithm are proven. Finally, all these results are applied on a LDM with AR$(1)$ residuals.

Keywords: Records, δ-Records, Asymptotics, Central Limit Theorem, Law of Iterated Logarithm


Stochastic Processes
November 7, 2023  4:50 PM
CC2: Conference Room

Other papers in the same session

Cadenas de Markov finitas y polinomios ortogonales

J. Díaz, A. Branquinho, A. Foulquié Moreno, M. Mañas

Cookie policy

We use cookies in order to be able to identify and authenticate you on the website. They are necessary for the correct functioning of it, and therefore they can not be disabled. If you continue browsing the website, you are agreeing with their acceptance, as well as our Privacy Policy.

Additionally, we use Google Analytics in order to analyze the website traffic. They also use cookies and you can accept or refuse them with the buttons below.

You can read more details about our Cookie Policy and our Privacy Policy.