Last modified: 2018-05-16

#### Abstract

Let {X_n, n âˆˆ N} be a stationary sequence of random variables in R with common continuous distribution F. For j âˆˆ N, let M_j = max(X_1,...,X_j), then we say that Xn is a record if X_n > M_{nâˆ’1}. Single and joint records have been extensively studied in the case that X_1, X_2, ... are independent (Galambos 1987, Arnold, Balakrishnan, and Nagaraja 1998, Falk, Khorrami, and Padoan 2017). Instead, few results are known when dependence among variables is taken into account. We derive the stochastic behaviour of records in the case that X_1,X_2,... are dependent, under appropriate conditions on the dependence structure.

#### References

Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja (1998). Records. Wiley Series in Probability and Statistics. New York: Wiley.

Falk, M., A. Khorrami, and S. A. Padoan (2017). Some results on joint record events. Statistics and Probability Letters 135(11â€“19).

Galambos, J. (1987). The Asymptotic Theory of Extreme Order Statistics (2 ed.). Malabar: Krieger.