The paper deals with the renewal risk model. A precise large deviation result in the case of subexponential claim sizes is proved. As a special case, the example of Pareto distributed claim sizes and inter-occurrence times is investigated.

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...

The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis, Robinson and Surgailis (1999). We consider methods based on the partial sums of the squared observations which are similar in spirit to the classical R/S...

We prove the consistency of a family of CUSUM-type estimators of the point of change in the mean of dependent observations and derive the rates of convergence. The result is valid under weak assumptions on the dependence structure.