4 CL ´ EMENT DOMBRY, MICHAEL FALK, MAXIMILIAN ZOTT Outline and terminology. In this paper, we deal with different kinds of records of stochastic processes, generally assuming they are in the max-domain of attraction of an MSP and have continuous univariate marginal df. Let X , X $^{(1)}$, X $^{(2)}$, . . . be an iid sequence of stochastic processes in C ( S ). We call X ( n ) a simple record, if X ( n ) ̸≤ max$_{i}$$_{=1}$$_{,...,n}$$_{−}$$_{1}$ X ( i $^{)}$, and a complete record, if X ( n ) > max$_{i}$$_{=1}$$_{,...,n}$$_{−}$$_{1}$ X ( i $^{)}$. We further define By definition, the first observation X (1) is always a record, so we demand ¯ π$_{1}$ ( X ) = ¯ π$_{1}$ ( X ) = 1. In the univariate case, where X, X $^{(1)}$, X$^{(2)}$, . . . are simply random variables on the real line, records are much easier to handle, and clearly ¯ π$_{n}$ ( X ) = ¯ π$_{n}$ ( X ) = 1 $_{n}$. There are many detailed works on univariate record and record times, see Galambos (1987, Sections 6.2 and 6.3) and Arnold et al. (1998). Multivariate records have not been discussed that extensively, yet they haven been approached by e. g. Goldie and Resnick (1989), Goldie and Resnick (1995) or Arnold et al. (1998, Chapter 8). A concept that is closely related to the field of complete records is the so- called concurrency of extremes, which is due to Dombry et al. (2015). We say that X $^{(1)}$, . . . , X ( n ) are sample concurrent, if In that case, we call X ( k ) the champion among X $^{(1)}$, . . . , X ( n $^{)}$. We denote the sample concurrence probability by p$_{n}$ ( X ) and obtain due to the iid property p$_{n}$ ( X ) = P ( n ⋃ i =1 { X ( i ) > max 1 ≤ j = i ≤ $_{n}$X ( j ) } ) (4) = n ∑ i =1 P ( X ( i ) > max 1 ≤ j = i ≤ $_{n}$X ( j ) ) = nP ( X ( n ) > max j =1 ,...,n − $_{1}$X ( j ) ) = n ¯ π$_{n}$ ( X ) . max i =1 $_{,...,n}$X ( i ) = X ( k ) for some k ∈ { 1 , . . . , n } . ¯ π$_{n}$ ( X ) := P ( X ( n ) is a simple record ) , π$_{n}$ ( X ) := P X ( n ) is a complete record ) .