Invariance Principles for Paced Record Times and Applications

Let {Yn:n≥0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(t):t≥0} be a point process. In this paper, making use of strong invariance principles, we establish limit laws for the paced record process {X(t):t≥0} based on {Yn:n≥0} and {N(t):t≥0}. We consider as applications of our main results, the case of the classical and paced record models. We conclude by extensions of our theorems to non-homogeneous record processes.