ABSTRACT
Sums and maxima are usually seen as objects of a completely different nature. What can be placed between the sum Sn = X1 + · · · + Xn and the maximum Mn = max{Xi : 1 ≤ i ≤ n}? We believe that statistic
Rn(k) = max 0≤i≤n−k
(Xi+1 + · · · + Xi+k)
is a natural candidate to fill the gap. In this chapter we study the distribution of the maximum of partial sums
Rn(k).
