Jeanblanc et al. (Stochastic Process. Appl. 100 (2002) 223) give a representation of self-similar processes with independent increments by stochastic integrals with respect to background driving Lévy processes. Via Lamperti's transformation these processes correspond to stationary...

Abstract We propose an offline change detection method for the famous Cox–Ingersoll–Ross model based on a continuous sample. We develop one- and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete...

In this paper the integer-valued autoregressive model of order one, contaminated with additive outliers is studied in some detail. Moreover, parameter estimation is also addressed. Supposing that the timepoints of the outliers are known but their sizes are unknown, we prove that the conditional...

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

It is shown that the suitably normalized maximum likelihood estimators of some parameters of multidimensional Ornstein-Uhlenbeck processes with coefficient matrix of a special structure have exactly a normal distribution. This result provides a generalization to an arbitrary dimension of the...

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, where the autoregressive coefficients are equal, and their sum tends to one. It is shown that the limiting distribution of the least-squares estimator for this coefficient is normal and, in contrast to the...

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow...