Large deviation asymptotics for continued fraction expansions

We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and lower fluctuation process. Also a large deviation asymptotic for single digits is given.Comment: 15 page

Limit laws for distorted return time processes for infinite measure preserving transformations

We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition. We identify two critical cases for which we prove uniform distribution laws. For this we introduce the notion of uniformly returning sets and discuss some of their properties.Comment: 18 pages, 2 figure

Duchenne and Becker Muscular Dystrophy: Contribution of a Molecular and Immunohistochemical Analysis in Diagnosis in Morocco

Duchenne muscular dystrophy (DMD) and Becker muscular dystrophy (BMD) are X-linked recessive disorders caused by mutations of the DMD gene located at Xp21. In DMD patients, dystrophin is virtually absent; whereas BMD patients have 10% to 40% of the normal amount. Deletions in the dystrophin gene represent 65% of mutations in DMD/BMD patients. To explain the contribution of immunohistochemical and genetic analysis in the diagnosis of these dystrophies, we present 10 cases of DMD/BMD with particular features. We have analyzed the patients with immunohistochemical staining and PCR multiplex to screen for exons deletions. Determination of the quantity and distribution of dystrophin by immunohistochemical staining can confirm the presence of dystrophinopathy and allows differentiation between DMD and BMD, but dystrophin staining is not always conclusive in BMD. Therefore, only identification involved mutation by genetic analysis can establish a correct diagnosis

Distributionale Konvergenzsätze in unendlicher Ergodentheorie

Conservative ergodic measure preserving transformations on infinite measure spaces are considered. The asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition are investigated. As applications we derive asymptotic laws for the normalized Kac process and the normalized spent time Kac process. The notion of uniformly returning sets is introduced. For these sets it is proven that if the wandering rate is slowly varying then the normalized spent time Kac process converges strongly distributional to a random variable uniformly distributed on the unit interval.As a number theoretical application the continued fraction digits are considered as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalized linearly a large deviation asymptotic is proved

Distributional laws in infinite ergodic theory

Conservative ergodic measure preserving transformations on infinite measure spaces are considered. The asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition are investigated. As applications we derive asymptotic laws for the normalized Kac process and the normalized spent time Kac process. The notion of uniformly returning sets is introduced. For these sets it is proven that if the wandering rate is slowly varying then the normalized spent time Kac process converges strongly distributional to a random variable uniformly distributed on the unit interval.As a number theoretical application the continued fraction digits are considered as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalized linearly a large deviation asymptotic is proved