Let [zeta]nse be the adaptive polygonal process of self-normalized partial sums Sk=[summation operator]1[less-than-or-equals, slant]i[less-than-or-equals, slant]kXi of i.i.d. random variables defined by linear interpolation between the points (Vk2/Vn2,Sk/Vn), k[less-than-or-equals, slant]n,...

Let be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space and , , be the summation processes based on the collection of sets [0,t1]x...x[0,td], 0<=ti<=1, i=1,...,d. When d>=2, we characterize the weak convergence of in the Hölder space by the finiteness of the weak p...</=ti<=1,>

For quasi-associated random fields (comprising negatively and positively dependent fields) on we use Stein's method to establish the rate of normal approximation for partial sums taken over arbitrary finite subsets of .

Let {Xk:k≥1} be a linear process with values in the separable Hilbert space L2(μ) given by Xk=∑j=0∞(j+1)−Dεk−j for each k≥1, where D is defined by Df={d(s)f(s):s∈S} for each f∈L2(μ) with d:S→R and {εk:k∈Z} are independent and identically distributed L2(μ)-valued random...