In this paper we establish a local precise large deviation result for sums Sn, n=1,2,... of independent and identically distributed random variables X1,X2,... with O-regularly varying densities f. The asymptotic behavior of the probability is comparable, for fixed T, with quantities or...

This paper deals with the asymptotic behavior for the tail probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.

In this paper, we consider the randomly weighted sum S2Θ=Θ1X1+Θ2X2, where the two primary random summands X1 and X2 are real-valued and dependent with long or dominatedly varying tails, and the random weights Θ1 and Θ2 are positive, with values in [a,b], 0a≤b∞, and arbitrarily...

In this paper, we study a general stochastic trend model and provide conditions on the partial sums which imply the convergence of the V/S statistic. These conditions generalize those in Giraitis et al. (J. Appl. Probab. 38 (2001) 1033) obtained in the case of deterministic trend model. As a...

A relatively simple frequency-type testing procedure for unit root potentially contaminated by an additive stationary noise is introduced, which encompasses general settings and allows for linear trends. The proposed test for unit root versus stationarity is based on a finite number of...