STATISTICAL PROPERTIES OF LINEAR FRACTAL INTERPOLATION FUNCTIONS FOR RANDOM DATA SETS

Let N be an integer greater than or equal to 2 and let x'(i)s be numbers with x(0) < x(1) < x(2) < ...< x(N). Denote that I is the interval left perpendicularx(0), x(N)right perpendicular and Delta = {(x(k), mu(k)) is an element of R x R : k = 0, 1,..., N} is a set of points. Suppose that Y-k is a random perturbation of mu(k) for k = 0, 1,..., N, and we set Delta* = {(x(k), Y-k) : k = 0, 1,..., N}. Let f(Delta) and f(Delta*) be linear fractal interpolation functions on I corresponding to the set of points Delta and Delta*, respectively. The value f(Delta*)(x) is random for all x is an element of I. In this paper, we show that the expectation of f(Delta*)(x) is f(Delta)(x). We also establish estimations for the variance of f(Delta*)(x) and the expectation of |f(Delta*)(x) - f(Delta)(x)|.