On the almost sure limit theorem for the joint version of maxima and minima of non-stationary random fields

Abstract

We obain an almost sure limit theorem for the joint version of maxima and minima of a non-stationary random field defined over discrete subsets of ${\mathbb{R}}^2,$ under some dependence conditions.

Keywords:

• Extremes of random fields
• almost sure limit theorem
• coordinatewise-mixing condition

Acknowledgments

We are grateful to the referee for the detailed comments and suggestions which helped the final form of this paper.

Additional information

Funding

This work was supported by National Foundation of Science and Technology through UID/MAT/00212/2020.