In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution ofand which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function L(t) is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis.

Abstract. In this paper we propose a periodic, mean-reverting Ornstein-Uhlenbeck process of the form dX t = (L(t) − α X t ) dt + σ dB t , t ≥ 0, where L(t) is a periodic, parametric function. We apply maximum likelihood estimation for the drift parameters based on time-continuous observations. The estimator is given explicitly and we prove strong consistency and asymptotic normality as the observed number of periods tends to infinity. The essential idea of the asymptotic study is the interpretation of the stochastic process as a sequence of random variables that take values in some function space.

Abstract. This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein-Uhlenbeck-type jump diffusion, which is a widely used model, we prove consistency of our estimator.

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