FUNCTIONAL LIMIT THEOREMS IN HOLDER SPACE FOR RESIDUALS OF NEARLY NONSTATIONARY AR (1) PROCESS

We investigate the polygonal line process built on the residuals of the first order nearly nonstationary autoregressive process. We prove functional limit theorems in Holder space in two cases: the autoregressive coefficient phi(n) is defined as e(gamma/n) , gamma < 0 is a constant, and phi(n) is defined as 1 - gamma(n) / n, gamma(n) -> infinity, and gamma(n) / n tends to zero as n -> infinity. Also we discuss some applications of these functional limit theorems in epidemic change detection.